|
%I #14 May 13 2022 04:54:59
%S 1,3,2,3,7,6,6,5,8,9,6,15,10,14,18,8,12,12,15,14,24,11,21,18,12,31,18,
%T 30,18,30,20,15,42,24,26,36,17,24,36,18,31,35,24,42,20,21,56,33,30,45,
%U 28,42,32,36,30,63,39,54,26,48,27,70,54,38,62,60,36,45,36,90,42,56,78
%N Sigma(k)/4 when k is not a sum of 2 squares.
%C Conjecture : if n is not the sum of 2 squares sigma(n) == 0 (mod 4) (converse is not true : if sigma(n) == 0 (mod 4), n is sometimes the sum of 2 squares : sigma(65) = 84 == 0 (mod 4) but 65 = 49+16 is a sum of 2 squares).
%H Amiram Eldar, <a href="/A071010/b071010.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = sigma(A022544(n))/4.
%t DivisorSigma[1, Select[Range[120], SquaresR[2, #] == 0 &]]/4 (* _Amiram Eldar_, May 13 2022 *)
%o (PARI) for(n=0,200,if(sum(i=0,n,sum(j=0,i,if(i^2+j^2-n,0,1)))==0,print1(sigma(n)/4,",")))
%Y Cf. A000203, A022544.
%K easy,nonn
%O 1,2
%A _Benoit Cloitre_, May 19 2002
|
