A339748 a(n) = (6^(valuation(n, 6) + 1) - 1) / 5.

1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 43, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 43, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1

Offset: 1

Author

Ilya Gutkovskiy, Dec 15 2020

Keywords

• nonn

Comments

Sum of powers of 6 dividing n.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A038712, A080278, A088842, A122841, A234959, A323921, A339747.

Programs

Mathematica

Table[(6^(IntegerExponent[n, 6] + 1) - 1)/5, {n, 1, 100}]
nmax = 100; CoefficientList[Series[Sum[6^k x^(6^k)/(1 - x^(6^k)), {k, 0, Floor[Log[6, nmax]] + 1}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{k>=0} 6^k * x^(6^k) / (1 - x^(6^k)).

L.g.f.: -log(Product_{k>=0} (1 - x^(6^k))).

Dirichlet g.f.: zeta(s) / (1 - 6^(1 - s)).