9801 (number)

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← 980098019802 →
Cardinal nine thousand eight hundred one
Ordinal 9801st
(nine thousand eight hundred first)
Factorization 34 × 112
Divisors 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801
Greek numeral ,ΘΩΑ´
Roman numeral IXDCCCI, ixdccci
Binary 100110010010012
Ternary 1111100003
Senary 1132136
Octal 231118
Duodecimal 580912
Hexadecimal 264916

9801 (nine thousand eight hundred [and] one) is the natural number following 9800 and preceding 9802.

Contents

In mathematics

9801 is most notable for being the third, and only 4-digit square pentagonal number, [1] [2] since 9801 is a square number, which can be written as: , and it is also a pentagonal number, since it can also be written as: . [3] 9801 is also the number that is below 10,000 which are integral multiples of their reversals. [a] The only other number which has this property is 8712. [6] [7] [4] 9801 is the sixth number such as the binomial coefficient [b] is a perfect square. [8] 9801 is a part of one of the first few pairs of consecutive powerful numbers with 9800 (9800, 9801). [9] [10]

Notes

  1. ↑ It is also known as a palintiple. [4] [5]
  2. ↑ Which is: [8]

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA036353(Square pentagonal numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Weisstein, Eric W. "Pentagonal Square Number". mathworld.wolfram.com. Retrieved 2026-08-05.
  3. ↑ Çevik, Mehmet (2024-08-20). On Triangular Pentagonal and Square Pentagonal Numbers (PDF). Duvar Yayınları. p. 53. ISBN   978-625-6069-53-4 . Retrieved 2026-08-06.
  4. 1 2 Sloane, N. J. A. (ed.). "SequenceA031877(Nontrivial reversal numbers (numbers which are integer multiples of their reversals), excluding palindromic numbers and multiples of 10.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Holt, Benjamin V. (2014), "Some general results and open questions on palintiple numbers", Integers, 14: A42, MR   3256704 .
  6. ↑ Weisgerber, Simon (2024-02-14). "Value Judgments in Mathematics: G. H. Hardy and the (Non-)seriousness of Mathematical Theorems". Global Philosophy. 34 (1): 1. doi:10.1007/s10516-023-09705-y. ISSN   2948-1538. PMC   10878122 .
  7. ↑ Friedman, Erich. "What's Special About This Number?" . Retrieved 2026-08-07.
  8. 1 2 Koninck, J. M. de (2009). Those fascinating numbers. Internet Archive. Providence, R.I. : American Mathematical Society. ISBN   978-0-8218-4807-4.
  9. ↑ Weisstein, Eric W. "Powerful Number". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-11.
  10. ↑ "The Prime Glossary: powerful number". t5k.org. Retrieved 2026-09-11.
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