A373216 Expansion of Sum_{k>=0} x^(6^k) / (1 - x^(6^k)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3

Offset: 1

Author

Seiichi Manyama, May 28 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001511, A051064, A055457, A115362, A373217.

Cf. A122841, A373220.

Programs

PARI

a(n) = valuation(n, 6)+1;

Formula

G.f. A(x) satisfies A(x) = x/(1 - x) + A(x^6).

a(6*n+1) = a(6*n+2) = ... = (6*n+5) = 1 and a(6*n+6) = 1 + a(n+1) for n >= 0.

a(n) = A122841(n) + 1.

G.f.: Sum_{i>=1, j>=0} x^(i*6^j). - Seiichi Manyama, Mar 23 2025

a(n) = A122841(6*n). - R. J. Mathar, Jun 28 2025