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Odd abundant numbers k for which sigma(k) == 3 (mod 4).
8

%I #14 Apr 05 2024 04:43:42

%S 11025,99225,245025,540225,893025,1334025,2205225,3980025,4862025,

%T 5832225,6890625,8037225,8555625,9828225,10595025,10989225,12006225,

%U 14402025,19847025,20385225,24354225,26163225,26471025,29648025,31979025,35820225,38378025,43758225,46580625,49491225,50339025,52490025,55577025,57836025,60140025

%N Odd abundant numbers k for which sigma(k) == 3 (mod 4).

%C These are all squares. Square roots are in A325312.

%H Antti Karttunen, <a href="/A325311/b325311.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A325312(n)^2. - _Amiram Eldar_, Apr 05 2024

%t Select[Range[1, 7755, 2]^2, Mod[(s = DivisorSigma[1, #]), 4] == 3 && s > 2*# &] (* _Amiram Eldar_, Apr 05 2024 *)

%o (PARI) isA325311(n) = (n%2 && (3==sigma(n)%4) && sigma(n)>(2*n));

%Y Cf. A000203, A324647, A325312 (square roots).

%Y Intersection of A005231 and A324899.

%Y Subsequence of A156942.

%K nonn

%O 1,1

%A _Antti Karttunen_, Apr 20 2019