Original entry on oeis.org
1, 1, 2, 5, 12, 30, 80, 236, 782, 2872, 11551, 50208, 233475, 1153424, 6022129, 33094892, 190798443, 1150698311, 7241821945, 47455029775, 323155438297, 2282781968327, 16700909857189, 126356647220803, 987303496571557, 7957134024398329, 66071773173223712
Offset: 0
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)])
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