A065126 Numbers n for which sigma_2(n^2) == 3 (mod 10).

11, 19, 22, 29, 31, 33, 38, 41, 44, 55, 57, 58, 59, 61, 62, 66, 71, 76, 77, 79, 82, 87, 88, 89, 93, 95, 99, 101, 109, 110, 114, 116, 118, 122, 123, 124, 131, 132, 133, 139, 142, 143, 145, 149, 151, 152, 154, 155, 158, 164, 165, 171, 174, 176, 177, 178, 179, 181

Offset: 1

Author

Labos Elemer, Nov 21 2001

Keywords

• easy
• nonn

Comments

It appears that sigma_2( m^2 ) = 3 (mod 10) iff m is divisible by a prime p = 1 or 9 (mod 10), else sigma_2( m^2 ) = 1 (mod 10). - M. F. Hasler, May 14 2008

This seems also to be numbers whose square is expressible in only one way as x^2 + 3xy + y^2, with 0 < x < y. - Colin Barker, Dec 24 2014

Examples

			n=29: sigma[2,29^2] = sigma[2,841] = 708123 = 10.70812+3; among the numbers all residues modulo 8 occur.
		

Links

• M. F. Hasler, Table of n, a(n) for n=1..7747.

Crossrefs

Cf. A000290, A001157, A057660, A065803.

Programs

Mathematica

Select[Range[200],Mod[DivisorSigma[2,#^2],10]==3&] (* Harvey P. Dale, Oct 21 2011 *)

PARI

c=0; for( n=1,10^5,sigma(n^2,2)%5==3 & write("b065126.txt",c++" "n)) \\ M. F. Hasler, May 14 2008

Formula

Mod[DivisorSigma[2, n^2], 10]=3.

Extensions

More terms and better description from M. F. Hasler, May 14 2008