A336998 a(n) = n! * Sum_{d|n} 3^(d - 1) / d!.

1, 5, 15, 87, 201, 3123, 5769, 148347, 913761, 11541123, 39975849, 2616723387, 6227552241, 230557039443, 4151870901369, 76980002233707, 355687471142721, 27886053280896963, 121645100796252489, 10474674957482235867, 135117295282596928401, 2811664555920692775603

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..445

Formula

E.g.f.: Sum_{k>=1} (exp(3*x^k) - 1) / 3.

a(p) = p! + 3^(p - 1), where p is prime.

Mathematica

Table[n! Sum[3^(d - 1)/d!, {d, Divisors[n]}], {n, 1, 22}]
nmax = 22; CoefficientList[Series[Sum[(Exp[3 x^k] - 1)/3, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

Prog

(PARI) a(n) = n! * sumdiv(n, d, 3^(d-1)/d!); \\ Michel Marcus, Aug 12 2020
(Magma)
A336998:= func< n | Factorial(n)*(&+[3^(d-1)/Factorial(d): d in Divisors(n)]) >;
[A336998(n): n in [1..40]]; // G. C. Greubel, Jun 26 2024
(SageMath)
def A336998(n): return factorial(n)*sum(3^(k-1)/factorial(k) for k in (1..n) if (k).divides(n))
[A336998(n) for n in range(1, 41)] # G. C. Greubel, Jun 26 2024

Crossrefs

Cf. A034730, A053486, A057625, A336997.

Sequence in context: A058820 A054363 A211944 * A276474 A362577 A184438

Adjacent sequences: A336995 A336996 A336997 * A336999 A337000 A337001

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 10 2020

Status

approved