%I #14 Jul 30 2024 14:35:14

%S 1,30,105,120,132,231,252,380,495,520,595,616,630,680,756,858,870,924,

%T 1040,1155,1173,1365,1428,1463,1547,1610,1722,1768,1820,1953,1976,

%U 1995,2002,2016,2080,2093,2170,2184,2277,2310,2508,2520,2530,2552,2618,2622

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

%H Amiram Eldar, <a href="/A081370/b081370.txt">Table of n, a(n) for n = 1..10000</a>

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts#Binomial_coefficients_modulo_integers">PARI/GP Scripts for Miscellaneous Math Problems: Binomial coefficients modulo integers</a> (binomod.gp).

%t Do[s=Mod[Binomial[n^2, n], n^2]; If[s==0, Print[n]], {n, 1, 10000}]

%o (PARI) is(k) = binomod(k^2, k, k^2) == 0; \\ _Amiram Eldar_, Jul 30 2024, using _Max Alekseyev_'s binomod.gp

%Y Cf. A014062, A081369.

%K nonn

%O 1,2

%A _Labos Elemer_, Mar 20 2003