A081339 Numbers n such that sigma(n^2) modulo 4 = 1.

1, 3, 7, 9, 10, 11, 19, 20, 21, 23, 25, 26, 27, 30, 31, 33, 34, 40, 43, 47, 49, 52, 57, 58, 59, 60, 63, 65, 67, 68, 69, 70, 71, 74, 75, 77, 78, 79, 80, 81, 82, 83, 85, 90, 93, 99, 102, 103, 104, 106, 107, 110, 116, 120, 121, 122, 127, 129, 131, 133, 136, 139, 140, 141, 145

Offset: 1

Author

Benoit Cloitre, Apr 20 2003

Keywords

• nonn

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A065764, A081325.

Contains A004614.

Programs

Maple

filter:= proc(n) local F, t;
  F:= select(t -> t[1] mod 4 = 1, ifactors(n)[2]);
  (add(t[2],t=F) - n) mod 2 = 1;
end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 22 2017

Mathematica

Select[Range[150],Mod[DivisorSigma[1,#^2],4]==1&] (* Harvey P. Dale, Apr 07 2012 *)

PARI

isok(n) = (sigma(n^2) % 4) == 1; \\ Michel Marcus, Jan 22 2017