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A353238
Perfect powers that are divisible by 3.
2
9, 27, 36, 81, 144, 216, 225, 243, 324, 441, 576, 729, 900, 1089, 1296, 1521, 1728, 1764, 2025, 2187, 2304, 2601, 2916, 3249, 3375, 3600, 3969, 4356, 4761, 5184, 5625, 5832, 6084, 6561, 7056, 7569, 7776, 8100, 8649, 9216, 9261, 9801, 10404, 11025, 11664, 12321
OFFSET
1,1
COMMENTS
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).
LINKS
FORMULA
a(n) has the form (3*m)^k for some positive integer m := m(n) and some k > 1.
Sum_{n>=1} 1/a(n) = -Sum_{k>=2} mu(k)*zeta(k)/3^k = 0.2306128559... - Amiram Eldar, Jul 02 2022
EXAMPLE
36 is a term since 36 = (2*3)^2 is a power of a multiple of 3.
MAPLE
q:= n-> igcd(seq(i[2], i=ifactors(n)[2]))>1:
select(q, [9*i$i=1..2000])[]; # Alois P. Heinz, May 05 2022
MATHEMATICA
Select[9*Range[1400], GCD @@ FactorInteger[#][[All, 2]] > 1 &]
PROG
(PARI) isok(k) = ispower(k) && !(k % 3); \\ Michel Marcus, May 02 2022
CROSSREFS
Cf. A000244.
Intersection of A001597 and A008585.
Intersection of A001597 and A008591.
Other perfect powers: A075090 (even), A075109 (odd), A353152 (multiple of 5).
Sequence in context: A036303 A359030 A325299 * A116455 A103753 A238333
KEYWORD
nonn,easy
AUTHOR
Marco Ripà, May 02 2022
STATUS
approved