A136478 Smallest y such that for x = A136477(n), x^2 + x + y^2 is an odd primitive abundant number, A136476(n).

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

Offset: 1

Author

Pierre CAMI, Dec 31 2007

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A006038, A136476, A136477, A136479.

Programs

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

Formula

a(n) = sqrt(A136476(n) - A136477(n)^2 - A136477(n)). - M. F. Hasler, Feb 22 2017

Extensions

Edited by M. F. Hasler, Feb 22 2017