OFFSET
1,3
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
From Vaclav Kotesovec, Jun 25 2024: (Start)
Dirichlet g.f.: zeta(s) * (3^s/(3^s-1))^2.
Sum_{k=1..n} a(k) ~ 9*n/4 - log(n)*(log(n) + 2*log(6*Pi))/(4*log(3)^2). (End)
Multiplicative with a(p^e) = (e+1)*(e+2)/2 if p = 3 and 1 if p != 3. - Amiram Eldar, Jun 27 2024
MATHEMATICA
nmax = 105; CoefficientList[Series[Sum[k x^(3^(k - 1))/(1 - x^(3^(k - 1))), {k, 1, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x] // Rest
Table[Binomial[IntegerExponent[3 n, 3] + 1, 2], {n, 1, 105}]
PROG
(PARI) a(n) = {my(e = valuation(n, 3)); (e+1)*(e+2)/2; } \\ Amiram Eldar, Jun 27 2024
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
Ilya Gutkovskiy, Jun 05 2024
STATUS
approved