A186428 - OEIS

%I #18 Jan 22 2025 12:01:04

%S 0,1,1,3,1,7,1,7,4,1,1,11,1,15,19,15,1,28,1,37,5,31,1,31,6,21,13,31,1,

%T 13,1,31,1,43,39,20,1,27,27,67,1,3,1,7,7,55,1,71,8,73,31,87,1,91,19,

%U 39,73,67,1,61,1,39,33,63,45,7,1,67,85,129,1,157,1,45,109,51,93,21,1,31,40,91,1,123,13,51,43,151,1,49,15,7,109,103,51,151,1,113,25,124,1,73,1,141,123,115,1,3,1,133,51,111,1,111,7,121,121

%N a(n) = sigma(n^2) modulo sigma(n).

%C a(n)=1 iff n is prime. Apparently a(n)>2 for composite n's.

%H Antti Karttunen, <a href="/A186428/b186428.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F a(n) = A065764(n) mod A000203(n).

%t Table[Mod[DivisorSigma[1,n^2],DivisorSigma[1,n]],{n,200000}]

%o (PARI) A186428(n) = (sigma(n^2)%sigma(n)); \\ _Antti Karttunen_, Jan 22 2025

%Y Cf. A000203, A065764.

%K nonn,easy,changed

%O 1,4

%A _Zak Seidov_, Mar 06 2011