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%I #30 Jul 02 2022 09:28:21
%S 9,27,36,81,144,216,225,243,324,441,576,729,900,1089,1296,1521,1728,
%T 1764,2025,2187,2304,2601,2916,3249,3375,3600,3969,4356,4761,5184,
%U 5625,5832,6084,6561,7056,7569,7776,8100,8649,9216,9261,9801,10404,11025,11664,12321
%N Perfect powers that are divisible by 3.
%C Terms are multiples of 9, so that a(n) == 0 (mod 9) (since no perfect power divisible by 3 can have a 3-adic valuation below 2).
%H Amiram Eldar, <a href="/A353238/b353238.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) has the form (3*m)^k for some positive integer m := m(n) and some k > 1.
%F Sum_{n>=1} 1/a(n) = -Sum_{k>=2} mu(k)*zeta(k)/3^k = 0.2306128559... - _Amiram Eldar_, Jul 02 2022
%e 36 is a term since 36 = (2*3)^2 is a power of a multiple of 3.
%p q:= n-> igcd(seq(i[2], i=ifactors(n)[2]))>1:
%p select(q, [9*i$i=1..2000])[]; # _Alois P. Heinz_, May 05 2022
%t Select[9*Range[1400], GCD @@ FactorInteger[#][[All, 2]] > 1 &]
%o (PARI) isok(k) = ispower(k) && !(k % 3); \\ _Michel Marcus_, May 02 2022
%Y Cf. A000244.
%Y Intersection of A001597 and A008585.
%Y Intersection of A001597 and A008591.
%Y Other perfect powers: A075090 (even), A075109 (odd), A353152 (multiple of 5).
%K nonn,easy
%O 1,1
%A _Marco Ripà_, May 02 2022
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