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
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..445
Programs
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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
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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 -
PARI
a(n) = n! * sumdiv(n, d, 3^(d-1)/d!); \\ Michel Marcus, Aug 12 2020
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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
Formula
E.g.f.: Sum_{k>=1} (exp(3*x^k) - 1) / 3.
a(p) = p! + 3^(p - 1), where p is prime.