login
A339748
a(n) = (6^(valuation(n, 6) + 1) - 1) / 5.
3
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
1,6
COMMENTS
Sum of powers of 6 dividing n.
LINKS
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 15 2020
STATUS
approved