A363913 a(n) = Sum_{k=0..n} divides(k, n) * 3^k, where divides(k, n) = 1 if k divides n, otherwise 0.

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

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{j=0..n} A113704(j, n) * m^j for m = 3; for other cases see the crossreferences.

a(n) = 3*A034730(n), n>=1. - R. J. Mathar, Jul 04 2023

Maple

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);

Mathematica

A363913[n_]:= If[n==0, 1, 3*DivisorSum[n, 3^(#-1) &]];
Table[A363913[n], {n, 0, 40}] (* G. C. Greubel, Jun 26 2024 *)

Prog

(SageMath)
def a(n): return sum(3^k * k.divides(n) for k in srange(n+1))
print([a(n) for n in range(29)])
(Python)
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
(Magma)
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

Crossrefs

Cf. A000007 (m = 0), A000005 (m = 1), A055895 (m = 2), this sequence (m = 3).

Cf. A113704, A363733, A363734, A363735, A363421.

Sequence in context: A089143 A073952 A107231 * A352157 A293656 A131936

Adjacent sequences: A363910 A363911 A363912 * A363914 A363915 A363916

Keyword

nonn

Author

Peter Luschny, Jun 28 2023

Status

approved