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A116963 Inverse Moebius transform of the shifted tetrahedral numbers. 10
4, 14, 24, 49, 60, 118, 124, 214, 244, 356, 368, 608, 564, 814, 896, 1183, 1144, 1668, 1544, 2162, 2168, 2678, 2604, 3698, 3336, 4228, 4304, 5344, 4964, 6732, 5988, 7728, 7528, 8924, 8616, 11297, 9884, 12214, 12064, 14668, 13248, 17132, 15184, 18928, 18412, 21038 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) = Sum_{d|n} (d+1)*(d+2)*(d+3)/6 = Sum_{d|n} A000292(d+1).
G.f.: Sum_{k>0} (1/(1-x^k)^4 - 1). - Seiichi Manyama, Jun 12 2023
EXAMPLE
a(12) = ((1+1)*(1+2)*(1+3)/6) + ((2+1)*(2+2)*(2+3)/6) + ((3+1)*(3+2)*(3+3)/6) + ((4+1)*(4+2)*(4+3)/6) + ((6+1)*(6+2)*(6+3)/6) + ((12+1)*(12+2)*(12+3)/6) = 4 + 10 + 20 + 35 + 84 + 455 = 608.
a(13) = ((1+1)*(1+2)*(1+3)/6) + ((13+1)*(13+2)*(13+3)/6) = 4 + 560 = 564.
MATHEMATICA
a[n_] := DivisorSum[n, Binomial[# + 3, 3] &]; Array[a, 50] (* Amiram Eldar, Jul 05 2023 *)
PROG
(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, 1/(1-x^k)^4-1)) \\ Seiichi Manyama, Jun 12 2023
CROSSREFS
See also: A007437 (inverse Moebius transform of triangular numbers).
Sequence in context: A277591 A017317 A195973 * A094930 A289665 A080286
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 31 2006
STATUS
approved

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Last modified May 21 07:02 EDT 2024. Contains 372729 sequences. (Running on oeis4.)