A209804 a(n) = Sum_{d|n} d*3^(n*d).

3, 171, 59076, 172200087, 4236443047458, 900567812945319804, 1675095304614322707132768, 27469470562340107289343634221615, 3990838394187339929534246698449141509871, 5153775207320113310364614887146151186290992699106

Offset

1,1

Comments

Equals the logarithmic derivative of A209495.

Links

Table of n, a(n) for n=1..10.

Formula

L.g.f.: Sum_{n>=1} -log(1 - 3^(n^2)*x^n).

L.g.f.: log( Sum_{n>=0} 3^(n^2)*x^n / Product_{k=1..n} (1 - 3^(k^2)*x^k) ).

Example

L.g.f.: L(x) = 3*x + 171*x^2/2 + 59076*x^3/3 + 172200087*x^4/4 + ...
where exponentiation yields the g.f. of A209495:
exp(L(x)) = 1 + 3*x + 90*x^2 + 19953*x^3 + 43113141*x^4 + ...

Mathematica

a[n_] := DivisorSum[n, # * 3^(n*#) &]; Array[a, 10] (* Amiram Eldar, Aug 22 2023 *)

Prog

(PARI) {a(n)=sumdiv(n, d, d*3^(n*d))}
(PARI) {a(n)=n*polcoeff(sum(m=1, n, -log(1 - 3^(m^2)*x^m +x*O(x^n))), n)}
(PARI) {a(n)=n*polcoeff(log(1+sum(m=1, n, 3^(m^2)*x^m/prod(k=1, m, 1-(3^k*x)^k+x*O(x^n)))), n)}
for(n=1, 15, print1(a(n), ", "))

Crossrefs

Cf. A209495, A209803.

Sequence in context: A032484 A119117 A136473 * A306401 A053930 A053920

Adjacent sequences: A209801 A209802 A209803 * A209805 A209806 A209807

Keyword

nonn

Author

Paul D. Hanna, Mar 13 2012

Status

approved