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A318666
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a(n) = 2^{the 3-adic valuation of n}.
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2
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1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 16, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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Multiplicative with a(3^e) = 2^e, a(p^e) = 1 for any other primes.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - Amiram Eldar, Nov 17 2022
Dirichlet g.f.: zeta(s)*(3^s-1)/(3^s-2). - Amiram Eldar, Jan 03 2023
More precise asymptotics: Sum_{k=1..n} a(k) ~ 2*n + zeta(log(2)/log(3)) * n^(log(2)/log(3)) / (2*log(2)). - Vaclav Kotesovec, Jun 25 2024
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MATHEMATICA
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PROG
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(PARI) A318666(n) = 2^valuation(n, 3);
(PARI) A318666(n) = { my(f = factor(n), m=1); for(i=1, #f~, if(3 == f[i, 1], m *= 2^f[i, 2])); (m); };
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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