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%I #15 Jun 27 2022 11:07:06
%S 65,85,125,130,145,170,185,205,221,250,260,265,290,305,340,365,370,
%T 377,410,442,445,481,485,493,500,505,520,530,533,545,565,580,585,610,
%U 629,680,685,689,697,730,740,745,754,765,785,793,820,865,884,890,901,905
%N Numbers n such that n is a sum of 2 squares (i.e., n is in A001481(k)) and sigma(n) == 0 (mod 4).
%C It is conjectured that if m is not a sum of 2 squares (i.e., m is in A022544(k)) sigma(m) == 0 (mod 4).
%H Michael De Vlieger, <a href="/A071011/b071011.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[10^3], And[SquaresR[2, #] > 0, Divisible[DivisorSigma[1, #], 4]] &] (* _Michael De Vlieger_, Jul 30 2017 *)
%o (PARI) for(n=1,1000,if(1-sign(sum(i=0,n,sum(j=0,i,if(i^2+j^2-n,0,1))))+sigma(n)%4==0,print1(n,",")))
%o (Python)
%o from math import prod
%o from itertools import count, islice
%o from sympy import factorint
%o def A071011_gen(): # generator of terms
%o return filter(lambda n:(lambda f:all(p & 3 != 3 or e & 1 == 0 for p, e in f) and prod((p**(e+1)-1)//(p-1) & 3 for p, e in f) & 3 == 0)(factorint(n).items()),count(0))
%o A071011_list = list(islice(A071011_gen(),30)) # _Chai Wah Wu_, Jun 27 2022
%Y Cf. A001481, A022544.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, May 19 2002
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