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A339748 a(n) = (6^(valuation(n, 6) + 1) - 1) / 5. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Sum of powers of 6 dividing n.

LINKS

Table of n, a(n) for n=1..100.

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)).

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

CROSSREFS

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

Sequence in context: A010143 A101027 A129408 * A325470 A240831 A170824

Adjacent sequences:  A339745 A339746 A339747 * A339749 A339750 A339751

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 15 2020

STATUS

approved

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Last modified June 19 12:51 EDT 2021. Contains 345129 sequences. (Running on oeis4.)