A136477 Numbers x such that for some y < sqrt(2x), x^2 + x + y^2 is an odd primitive abundant number, A136476(n).

97, 112, 122, 135, 144, 179, 202, 207, 214, 217, 227, 354, 359, 477, 507, 569, 612, 632, 639, 732, 832, 2124, 2359, 2362, 2440, 2466, 2517, 2970, 3097, 3247, 3342, 3367, 3374, 3419, 3425, 3518, 3545, 3562, 3644, 3672, 3699, 3789, 3879, 3969, 3985, 4050

Offset: 1

Author

Pierre CAMI, Dec 31 2007

Keywords

• nonn

Comments

The corresponding y-values are listed in A136478. (Unlike the x-values listed here, y is not increasing with A136476(n).)

Examples

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

Crossrefs

Cf. A006038, A136476, A136478, A136479.

Programs

PARI

is(x,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)); return(1))} \\ M. F. Hasler, Feb 22 2017

Extensions

Edited by M. F. Hasler, Feb 22 2017