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Numbers n such that sigma(n^2) modulo 4 = 1.
2

%I #16 Jan 22 2017 13:34:37

%S 1,3,7,9,10,11,19,20,21,23,25,26,27,30,31,33,34,40,43,47,49,52,57,58,

%T 59,60,63,65,67,68,69,70,71,74,75,77,78,79,80,81,82,83,85,90,93,99,

%U 102,103,104,106,107,110,116,120,121,122,127,129,131,133,136,139,140,141,145

%N Numbers n such that sigma(n^2) modulo 4 = 1.

%C Numbers n such that the sum of exponents of primes == 1 (mod 4) in the prime factorization of n is not congruent to n mod 2. - _Robert Israel_, Jan 22 2017

%H Robert Israel, <a href="/A081339/b081339.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(n) local F, t;

%p F:= select(t -> t[1] mod 4 = 1, ifactors(n)[2]);

%p (add(t[2],t=F) - n) mod 2 = 1;

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Jan 22 2017

%t Select[Range[150],Mod[DivisorSigma[1,#^2],4]==1&] (* _Harvey P. Dale_, Apr 07 2012 *)

%o (PARI) isok(n) = (sigma(n^2) % 4) == 1; \\ _Michel Marcus_, Jan 22 2017

%Y Cf. A000203, A065764, A081325.

%Y Contains A004614.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Apr 20 2003