A364222 Expansion of Sum_{k>=0} 3^k * x^(3^k) / (1 - x^(3^k))^2.

1, 2, 6, 4, 5, 12, 7, 8, 27, 10, 11, 24, 13, 14, 30, 16, 17, 54, 19, 20, 42, 22, 23, 48, 25, 26, 108, 28, 29, 60, 31, 32, 66, 34, 35, 108, 37, 38, 78, 40, 41, 84, 43, 44, 135, 46, 47, 96, 49, 50, 102, 52, 53, 216, 55, 56, 114, 58, 59, 120, 61, 62, 189, 64, 65, 132, 67, 68, 138, 70, 71, 216, 73, 74

Offset

1,2

Links

Table of n, a(n) for n=1..74.

Formula

a(n) = n * A051064(n).

If n == 0 (mod 3), a(n) = n + 3 * a(n/3) otherwise a(n) = n.

From Amiram Eldar, Jul 14 2023: (Start)

Multiplicative with a(3^e) = (e+1)*3^e and a(p^e) = p*e if p != 3.

Dirichlet g.f.: (3^s/(3^s-3)) * zeta(s-1).

Sum_{k=1..n} a(k) ~ (3/4)*n^2. (End)

Mathematica

a[n_] := n * (IntegerExponent[n, 3] + 1); Array[a, 100] (* Amiram Eldar, Jul 14 2023 *)

Prog

(PARI) a(n) = n*(valuation(n, 3)+1);

Crossrefs

Cf. A007949, A051064, A327625.

Cf. A091512, A364223, A364224.

Sequence in context: A182505 A010465 A065630 * A319376 A110633 A240232

Adjacent sequences: A364219 A364220 A364221 * A364223 A364224 A364225

Keyword

nonn,mult,easy

Author

Seiichi Manyama, Jul 14 2023

Status

approved