%I #27 Sep 08 2022 08:45:07

%S 49,169,196,361,441,676,784,961,1225,1369,1444,1521,1764,1849,2704,

%T 3136,3249,3721,3844,3969,4225,4489,4900,5329,5476,5776,5929,6084,

%U 6241,7056,7396,8281,8649,9025,9409,10609,10816,11025,11881,12321,12544

%N Squares satisfying sigma(n)==0 (mod 3).

%C 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.

%C Squares in A067051. - _Michel Marcus_, Dec 26 2013

%H Amiram Eldar, <a href="/A074216/b074216.txt">Table of n, a(n) for n = 1..10000</a>

%F Conjecture: a(n) = A072864(n)^2. - _R. J. Mathar_, May 19 2020

%p 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

%t Select[Range[150]^2,Divisible[DivisorSigma[1,#],3]&] (* _Harvey P. Dale_, Jul 10 2012 *)

%o (PARI) isok(n) = issquare(n) && !(sigma(n) % 3); \\ _Michel Marcus_, Aug 17 2019

%o (Magma) [n: n in [1..14161]|IsSquare(n) and DivisorSigma(1,n) mod 3 eq 0 ]; // _Marius A. Burtea_, Aug 17 2019

%Y Cf. A067051, A065764.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Sep 17 2002