A359018
a(n) = Sum_{d|n} d * 3^(d-1).
Original entry on oeis.org
1, 7, 28, 115, 406, 1492, 5104, 17611, 59077, 197242, 649540, 2127364, 6908734, 22325632, 71744968, 229600123, 731794258, 2324583475, 7360989292, 23245426690, 73222477552, 230128420012, 721764371008, 2259438436708, 7060738412431, 22029510754258, 68630377423960
Offset: 1
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A359018:= func< n | (&+[3^(d-1)*d: d in Divisors(n)]) >;
[A359018(n): n in [1..40]]; // G. C. Greubel, Jun 26 2024
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a[n_] := DivisorSum[n, 3^(#-1)*# &]; Array[a, 27] (* Amiram Eldar, Aug 27 2023 *)
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a(n) = sumdiv(n, d, d*3^(d-1));
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my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-3*x^k)^2))
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def A359018(n): return sum(3^(k-1)*k for k in (1..n) if (k).divides(n))
[A359018(n) for n in range(1,41)] # G. C. Greubel, Jun 26 2024
A336998
a(n) = n! * Sum_{d|n} 3^(d - 1) / d!.
Original entry on oeis.org
1, 5, 15, 87, 201, 3123, 5769, 148347, 913761, 11541123, 39975849, 2616723387, 6227552241, 230557039443, 4151870901369, 76980002233707, 355687471142721, 27886053280896963, 121645100796252489, 10474674957482235867, 135117295282596928401, 2811664555920692775603
Offset: 1
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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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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
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a(n) = n! * sumdiv(n, d, 3^(d-1)/d!); \\ Michel Marcus, Aug 12 2020
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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
A363913
a(n) = Sum_{k=0..n} divides(k, n) * 3^k, where divides(k, n) = 1 if k divides n, otherwise 0.
Original entry on oeis.org
1, 3, 12, 30, 93, 246, 768, 2190, 6654, 19713, 59304, 177150, 532290, 1594326, 4785168, 14349180, 43053375, 129140166, 387440940, 1162261470, 3486843786, 10460355420, 31381236768, 94143178830, 282430075332, 847288609689, 2541867422664, 7625597504700, 22876797240210
Offset: 0
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A363913:= func< n | n eq 0 select 1 else 3*(&+[3^(d-1): d in Divisors(n)]) >;
[A363913(n): n in [0..40]]; // G. C. Greubel, Jun 26 2024
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divides := (k, n) -> ifelse(k = n or (k > 0 and irem(n, k) = 0), 1, 0):
a := n -> local j; add(divides(j, n) * 3^j, j = 0 ..n): seq(a(n), n = 0..28);
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A363913[n_]:= If[n==0, 1, 3*DivisorSum[n, 3^(#-1) &]];
Table[A363913[n], {n,0,40}] (* G. C. Greubel, Jun 26 2024 *)
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from sympy import divisors
def A363913(n): return sum(3**k for k in divisors(n,generator=True)) if n else 1 # Chai Wah Wu, Jun 28 2023
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def a(n): return sum(3^k * k.divides(n) for k in srange(n+1))
print([a(n) for n in range(29)])