%I #18 Aug 20 2023 10:50:42
%S 1,5,17,110,394,4884,18108,294384,2054736,27986400,160460640,
%T 5733590400,26029779840,727452230400,11030096851200,223495556659200,
%U 1579093018675200,83918534992588800,553210247226470400,32584767906539520000,463473994611898368000,10352822932220719104000
%N a(n) = n! * Sum_{k|n} (Sum_{j=1..k} 1/j); the k-sum is over the positive divisors, k, of n.
%F E.g.f.: Sum_{k>0} log(1-x^k)/(x^k-1). - _Vladeta Jovovic_, Aug 01 2004
%e 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.
%t a[n_] := n! * DivisorSum[n, HarmonicNumber[#] &]; Array[a, 20] (* _Amiram Eldar_, Aug 18 2023 *)
%o (PARI) a(n) = n!*sumdiv(n, k, sum(j=1, k, 1/j)); \\ _Michel Marcus_, Aug 20 2023
%Y Cf. A001008, A002805.
%K nonn
%O 1,2
%A _Leroy Quet_, Feb 05 2002
%E a(20)-a(22) from _Amiram Eldar_, Aug 18 2023
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