login
A065126
Numbers n for which sigma_2(n^2) == 3 (mod 10).
1
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
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
KEYWORD
easy,nonn
AUTHOR
Labos Elemer, Nov 21 2001
EXTENSIONS
More terms and better description from M. F. Hasler, May 14 2008
STATUS
approved