9801 (number)
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| 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.
In mathematics
[edit]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]
Notes
[edit]
References
[edit]- ↑ Sloane, N. J. A. (ed.). "Sequence A036353 (Square pentagonal numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Weisstein, Eric W. "Pentagonal Square Number". mathworld.wolfram.com. Retrieved 2026-08-05.
- ↑ 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.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A031877 (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.
- ↑ Holt, Benjamin V. (2014), "Some general results and open questions on palintiple numbers", Integers, 14: A42, MR 3256704.
- ↑ 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.
- ↑ Friedman, Erich. "What's Special About This Number?". Retrieved 2026-08-07.
- 1 2 Koninck, J. M. de (2009). Those fascinating numbers. Internet Archive. Providence, R.I. : American Mathematical Society. ISBN 978-0-8218-4807-4.
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