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%I #15 Dec 24 2014 14:43:27
%S 11,19,22,29,31,33,38,41,44,55,57,58,59,61,62,66,71,76,77,79,82,87,88,
%T 89,93,95,99,101,109,110,114,116,118,122,123,124,131,132,133,139,142,
%U 143,145,149,151,152,154,155,158,164,165,171,174,176,177,178,179,181
%N Numbers n for which sigma_2(n^2) == 3 (mod 10).
%C 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
%C 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
%H M. F. Hasler, <a href="/A065126/b065126.txt">Table of n, a(n) for n=1..7747</a>.
%F Mod[DivisorSigma[2, n^2], 10]=3.
%e n=29: sigma[2,29^2] = sigma[2,841] = 708123 = 10.70812+3; among the numbers all residues modulo 8 occur.
%t Select[Range[200],Mod[DivisorSigma[2,#^2],10]==3&] (* _Harvey P. Dale_, Oct 21 2011 *)
%o (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
%Y Cf. A000290, A001157, A057660, A065803.
%K easy,nonn
%O 1,1
%A _Labos Elemer_, Nov 21 2001
%E More terms and better description from _M. F. Hasler_, May 14 2008