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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
1, 5, 17, 110, 394, 4884, 18108, 294384, 2054736, 27986400, 160460640, 5733590400, 26029779840, 727452230400, 11030096851200, 223495556659200, 1579093018675200, 83918534992588800, 553210247226470400, 32584767906539520000, 463473994611898368000, 10352822932220719104000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
E.g.f.: Sum_{k>0} log(1-x^k)/(x^k-1). - Vladeta Jovovic, Aug 01 2004
EXAMPLE
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.
MATHEMATICA
a[n_] := n! * DivisorSum[n, HarmonicNumber[#] &]; Array[a, 20] (* Amiram Eldar, Aug 18 2023 *)
PROG
(PARI) a(n) = n!*sumdiv(n, k, sum(j=1, k, 1/j)); \\ Michel Marcus, Aug 20 2023
CROSSREFS
Sequence in context: A234797 A062586 A301641 * A197912 A203114 A198027
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 05 2002
EXTENSIONS
a(20)-a(22) from Amiram Eldar, Aug 18 2023
STATUS
approved

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Last modified April 22 10:51 EDT 2024. Contains 371897 sequences. (Running on oeis4.)