A373279 Expansion of Sum_{k>=0} x^(3^k) / (1 - 3*x^(3^k)).

1, 3, 10, 27, 81, 246, 729, 2187, 6571, 19683, 59049, 177174, 531441, 1594323, 4783050, 14348907, 43046721, 129140409, 387420489, 1162261467, 3486785130, 10460353203, 31381059609, 94143181014, 282429536481, 847288609443, 2541865834900, 7625597484987

Offset: 1

Author

Seiichi Manyama, May 30 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A187767, A373280, A373281, A373282, A373283.

Cf. A000244, A046211, A051064, A364222.

Programs

PARI

b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
a(n, k=3) = sumdiv(n, d, d*b(d, k));

Formula

G.f. A(x) satisfies A(x) = x/(1 - 3*x) + A(x^3).

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

a(n) = Sum_{d|n} d * A046211(d).