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

1,1

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000290, A001157, A057660, A065803.

Sequence in context: A366195 A328870 A244287 * A284783 A145059 A124139

Adjacent sequences: A065123 A065124 A065125 * A065127 A065128 A065129

Keyword

easy,nonn

Author

Labos Elemer, Nov 21 2001

Extensions

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

Status

approved