A136478 - OEIS

%I #9 Feb 23 2017 22:34:07

%S 7,7,3,15,15,15,7,3,5,7,3,15,15,27,3,15,3,27,15,27,13,3,49,17,55,27,

%T 27,15,53,77,63,77,15,45,15,69,45,77,15,57,75,27,75,63,55,75,49,85,7,3

%N Smallest y such that for x = A136477(n), x^2 + x + y^2 is an odd primitive abundant number, A136476(n).

%C See A136477 and A136476 for the x-values and the abundant numbers x^2 + x + y^2.

%F a(n) = sqrt(A136476(n) - A136477(n)^2 - A136477(n)). - _M. F. Hasler_, Feb 22 2017

%e 97^2+97+7^2 = 9555 = A136476(1) is an odd primitive abundant number, therefore a(1) = 7.

%o (PARI) {for(x=1, 5000, my(n=x^2+x+1, f); forstep(y=1, sqrtint(2*x), 2, sigma(n+=y*4-4, -1)>2 || next; for(i=1, #f=factor(n)[, 1], sigma(n\f[i], -1)>2 && next(2)); print1(y","); break))} \\ _M. F. Hasler_, Feb 22 2017

%Y Cf. A006038, A136476, A136477, A136479.

%K nonn

%O 1,1

%A _Pierre CAMI_, Dec 31 2007

%E Edited by _M. F. Hasler_, Feb 22 2017