A074216 Squares satisfying sigma(n)==0 (mod 3).

49, 169, 196, 361, 441, 676, 784, 961, 1225, 1369, 1444, 1521, 1764, 1849, 2704, 3136, 3249, 3721, 3844, 3969, 4225, 4489, 4900, 5329, 5476, 5776, 5929, 6084, 6241, 7056, 7396, 8281, 8649, 9025, 9409, 10609, 10816, 11025, 11881, 12321, 12544

Offset: 1

Author

Benoit Cloitre, Sep 17 2002

Keywords

• nonn

Comments

Seems to contain all numbers of form k^2*p^2 where p are primes in A002476, k is not congruent to p and >=1.

Squares in A067051. - Michel Marcus, Dec 26 2013

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A067051, A065764.

Programs

Magma

[n: n in [1..14161]|IsSquare(n) and DivisorSigma(1,n) mod 3 eq 0 ]; // Marius A. Burtea, Aug 17 2019

Maple

with(numtheory); A074216:=n->`if`(1-ceil(sigma(n^2)/3)+floor(sigma(n^2)/3)=1,n^2,NULL); seq(A074216(n), n=1..200); # Wesley Ivan Hurt, Dec 06 2013

Mathematica

Select[Range[150]^2,Divisible[DivisorSigma[1,#],3]&] (* Harvey P. Dale, Jul 10 2012 *)

PARI

isok(n) = issquare(n) && !(sigma(n) % 3); \\ Michel Marcus, Aug 17 2019

Formula

Conjecture: a(n) = A072864(n)^2. - R. J. Mathar, May 19 2020