cp's OEIS Frontend

A071011 Numbers n such that n is a sum of 2 squares (i.e., n is in A001481(k)) and sigma(n) == 0 (mod 4).

%I A071011 #15 Jun 27 2022 11:07:06
%S A071011 65,85,125,130,145,170,185,205,221,250,260,265,290,305,340,365,370,
%T A071011 377,410,442,445,481,485,493,500,505,520,530,533,545,565,580,585,610,
%U A071011 629,680,685,689,697,730,740,745,754,765,785,793,820,865,884,890,901,905
%N A071011 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 A071011 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 A071011 Michael De Vlieger, <a href="/A071011/b071011.txt">Table of n, a(n) for n = 1..10000</a>
%t A071011 Select[Range[10^3], And[SquaresR[2, #] > 0, Divisible[DivisorSigma[1, #], 4]] &] (* _Michael De Vlieger_, Jul 30 2017 *)
%o A071011 (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 A071011 (Python)
%o A071011 from math import prod
%o A071011 from itertools import count, islice
%o A071011 from sympy import factorint
%o A071011 def A071011_gen(): # generator of terms
%o A071011     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 A071011_list = list(islice(A071011_gen(),30)) # _Chai Wah Wu_, Jun 27 2022
%Y A071011 Cf. A001481, A022544.
%K A071011 easy,nonn
%O A071011 1,1
%A A071011 _Benoit Cloitre_, May 19 2002