%I #38 Feb 14 2021 08:10:51

%S 1,39,793,2379,7137,76921,230763,692289,2076867,8329831,24989493,

%T 53695813,74968479,161087439,224905437,243762649,324863409,375870691,

%U 483262317,731287947,1127612073,1449786951,2094136707,2193863841,2631094837,3382836219,3606816823

%N Numbers k such that sigma(k^2) and Sum_{d|k} d*sigma(d) are both multiples of k.

%C Intersection of A069520 and A232354.

%C Can these numbers be characterized as the terms of A232354 which do not have a factor in {11, 1093, ...}? Is this A090814, or (a subsequence of) A126197?

%H Donovan Johnson, <a href="/A232067/b232067.txt">Table of n, a(n) for n = 1..70</a>

%t fQ[n_] := Mod[DivisorSigma[1, n^2], n] == 0 && Mod[DivisorSum[n, #*DivisorSigma[1, #] &], n] == 0; Select[Range[100000], fQ] (* _T. D. Noe_, Nov 25 2013 *)

%Y Cf. A000203, A069520, A232354.

%K nonn

%O 1,2

%A _M. F. Hasler_, Nov 24 2013