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

1,1

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

Formula

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

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 *)

Prog

(PARI) isok(n) = issquare(n) && !(sigma(n) % 3); \\ Michel Marcus, Aug 17 2019
(Magma) [n: n in [1..14161]|IsSquare(n) and DivisorSigma(1, n) mod 3 eq 0 ]; // Marius A. Burtea, Aug 17 2019

Crossrefs

Cf. A067051, A065764.

Sequence in context: A009409 A009431 A226353 * A216870 A254624 A256074

Adjacent sequences: A074213 A074214 A074215 * A074217 A074218 A074219

Keyword

nonn

Author

Benoit Cloitre, Sep 17 2002

Status

approved