A081370 Numbers k such that binomial(k^2, k) reduced mod k^2 is 0.

1, 30, 105, 120, 132, 231, 252, 380, 495, 520, 595, 616, 630, 680, 756, 858, 870, 924, 1040, 1155, 1173, 1365, 1428, 1463, 1547, 1610, 1722, 1768, 1820, 1953, 1976, 1995, 2002, 2016, 2080, 2093, 2170, 2184, 2277, 2310, 2508, 2520, 2530, 2552, 2618, 2622

Offset: 1

Author

Labos Elemer, Mar 20 2003

Keywords

• nonn
• changed

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: Binomial coefficients modulo integers (binomod.gp).

Crossrefs

Cf. A014062, A081369.

Programs

Mathematica

Do[s=Mod[Binomial[n^2, n], n^2]; If[s==0, Print[n]], {n, 1, 10000}]
Select[Range[3000],Mod[Binomial[#^2,#],#^2]==0&] (* Harvey P. Dale, Aug 26 2025 *)

PARI

is(k) = binomod(k^2, k, k^2) == 0; \\ Amiram Eldar, Jul 30 2024, using Max Alekseyev's binomod.gp