A067710 a(n) = n! * Sum_{k|n} (Sum_{j=1..k} 1/j); the k-sum is over the positive divisors, k, of n.
1, 5, 17, 110, 394, 4884, 18108, 294384, 2054736, 27986400, 160460640, 5733590400, 26029779840, 727452230400, 11030096851200, 223495556659200, 1579093018675200, 83918534992588800, 553210247226470400, 32584767906539520000, 463473994611898368000, 10352822932220719104000
Offset: 1
Keywords
Examples
a(6) = 6! *(1 + (1 + 1/2) + (1 + 1/2 + 1/3) + (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6)) because 1, 2, 3 and 6 are the divisors of 6.
Programs
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Mathematica
a[n_] := n! * DivisorSum[n, HarmonicNumber[#] &]; Array[a, 20] (* Amiram Eldar, Aug 18 2023 *)
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PARI
a(n) = n!*sumdiv(n, k, sum(j=1, k, 1/j)); \\ Michel Marcus, Aug 20 2023
Formula
E.g.f.: Sum_{k>0} log(1-x^k)/(x^k-1). - Vladeta Jovovic, Aug 01 2004
Extensions
a(20)-a(22) from Amiram Eldar, Aug 18 2023