58 (number)

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← 57 58 59 →
Cardinal fifty-eight
Ordinal 58th
(fifty-eighth)
Factorization 2 × 29
Divisors 1, 2, 29, 58
Greek numeral ΝΗ´
Roman numeral LVIII
Binary 1110102
Ternary 20113
Senary 1346
Octal 728
Duodecimal 4A12
Hexadecimal 3A16

58 (fifty-eight) is the natural number following 57 and preceding 59.

Contents

In mathematics

58 is a composite number, meaning its factor is 1, 2, 29, and 58. [1] Other than 1 and the number itself, 58 can be formed by multiplying two primes 2 and 29, making it a semiprime. [2] 58 is not divisible by any square number other than 1, making it a square-free integer [3] A semiprime that is not square numbers is called a squarefree semiprime, and 58 is among them. [4]

58 is equal to the sum of the first seven consecutive prime numbers: [5]

This is a difference of 1 from the seventeenth prime number and seventh super-prime, 59. [6] [7] 58 has an aliquot sum of 32 [8] within an aliquot sequence of two composite numbers (58, 32, 13, 1, 0) in the 13-aliquot tree. [9] There is no solution to the equation , making fifty-eight the sixth noncototient; [10] however, the totient summatory function over the first thirteen integers is 58. [11] [a]

On the other hand, the Euler totient of 58 is the second perfect number (28), [13] where the sum-of-divisors of 58 is the third unitary perfect number (90).

58 is also the second non-trivial 11-gonal number, after 30. [14]

58 represents twice the sum between the first two discrete biprimes 14 + 15 = 29, with the first two members of the first such triplet 33 and 34 (or twice 17, the fourth super-prime) respectively the twenty-first and twenty-second composite numbers, [15] and 22 itself the thirteenth composite. [15] (Where also, 58 is the sum of all primes between 2 and 17.) The first triplet is the only triplet in the sequence of consecutive discrete biprimes whose members collectively have prime factorizations that nearly span a set of consecutive prime numbers.

is also semiprime (the second such number for after 2). [16]

The fifth repdigit is the product between the thirteenth and fifty-eighth primes,

58 is also the smallest integer in decimal whose square root has a simple continued fraction with period 7. [17] It is the fourth Smith number whose sum of its digits is equal to the sum of the digits in its prime factorization (13). [18]

Given 58, the Mertens function returns , the fourth such number to do so. [19] The sum of the first three numbers to return zero (2, 39, 40) sum to 81 = 9 2, which is the fifty-eighth composite number. [15]

In science

Other fields

Base Hexxagon starting grid, with fifty-eight "usable" cells Hexxagon.png
Base Hexxagōn starting grid, with fifty-eight "usable" cells

58 is the number of usable cells on a Hexxagon game board.

Notes

  1. ↑ 58 is also the partial sum of the first eight records set by highly totient numbers m with values φ(m) = n: {2, 3, 4, 5, 6, 10, 11, 17}. [12]

Related Research Articles

15 (fifteen) is the natural number following 14 and preceding 16.

21 (twenty-one) is the natural number following 20 and preceding 22.

33 (thirty-three) is the natural number following 32 and preceding 34.

70 (seventy) is the natural number following 69 and preceding 71.

90 (ninety) is the natural number following 89 and preceding 91.

29 (twenty-nine) is the natural number following 28 and preceding 30. It is a prime number.

35 (thirty-five) is the natural number following 34 and preceding 36.

86 (eighty-six) is the natural number following 85 and preceding 87.

34 (thirty-four) is the natural number following 33 and preceding 35.

46 (forty-six) is the natural number following 45 and preceding 47.

64 (sixty-four) is the natural number following 63 and preceding 65.

92 (ninety-two) is the natural number following 91 and preceding 93

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

135 is the natural number following 134 and preceding 136.

<span class="mw-page-title-main">146 (number)</span> Natural number

146 is the natural number following 145 and preceding 147.

168 is the natural number following 167 and preceding 169.

177 is the natural number following 176 and preceding 178.

240 is the natural number following 239 and preceding 241.

888 is the natural number following 887 and preceding 889.

References

  1. ↑ Anjema, Henry (1767). Table of divisors of all the natural numbers from 1. to 10000. p.  3. ISBN   9781140919421 – via the Internet Archive.
  2. ↑ Neil, Sloane; Guy, R. K. (22 August 2010). "A001358: Semiprimes (or biprimes): products of two primes". On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  3. ↑ Sloane, Neil (n.d.). "A005117: Squarefree numbers: numbers that are not divisible by a square greater than 1". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 April 2024.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA006881(Semiprimes (or biprimes): products of two primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-05-07.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA007504(Sum of the first n primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2022-12-20.
  6. ↑ Sloane, N. J. A. (ed.). "SequenceA000040(The prime numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2022-12-20.
  7. ↑ Sloane, N. J. A. (ed.). "SequenceA006450(Prime-indexed primes: primes with prime subscripts.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2022-12-20.
  8. ↑ Sloane, N. J. A. (ed.). "SequenceA001065(Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-27.
  9. ↑ Sloane, N. J. A., ed. (1975). "Aliquot sequences". Mathematics of Computation. 29 (129). OEIS Foundation: 101–107. Retrieved 2024-02-27.
  10. ↑ "Sloane's A005278 : Noncototients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  11. ↑ Sloane, N. J. A. (ed.). "SequenceA002088(Sum of totient function.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-27.
  12. ↑ Sloane, N. J. A. (ed.). "SequenceA131934(Records in A014197.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-07-02.
  13. ↑ Sloane, N. J. A. (ed.). "SequenceA000010(Euler totient function.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-07-02.
  14. ↑ "Sloane's A051682 : 11-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  15. 1 2 3 Sloane, N. J. A. (ed.). "SequenceA002808(The composite numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-05-07.
  16. ↑ Sloane, N. J. A. (ed.). "SequenceA104494(Positive integers n such that n^17 + 1 is semiprime.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-27.
  17. ↑ "Sloane's A013646: Least m such that continued fraction for sqrt(m) has period n". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-03-18.
  18. ↑ "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  19. ↑ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
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