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A318249 a(n) = (n - 1)! * d(n), where d(n) = number of divisors of n (A000005).

%I A318249 #13 Nov 11 2020 03:09:09
%S A318249 1,2,4,18,48,480,1440,20160,120960,1451520,7257600,239500800,
%T A318249 958003200,24908083200,348713164800,6538371840000,41845579776000,
%U A318249 2134124568576000,12804747411456000,729870602452992000,9731608032706560000,204363768686837760000,2248001455555215360000,206816133911079813120000
%N A318249 a(n) = (n - 1)! * d(n), where d(n) = number of divisors of n (A000005).
%H A318249 Seiichi Manyama, <a href="/A318249/b318249.txt">Table of n, a(n) for n = 1..450</a>
%F A318249 E.g.f.: Sum_{k>=1} Sum_{j>=1} x^(j*k)/(j*k).
%F A318249 E.g.f.: -log(Product_{k>=1} (1 - x^k)^(1/k)).
%F A318249 E.g.f.: A(x) = log(B(x)), where B(x) = e.g.f. of A028342.
%F A318249 a(p^k) = (k + 1)*(p^k - 1)!, where p is a prime.
%t A318249 Table[(n - 1)! DivisorSigma[0, n], {n, 1, 24}]
%t A318249 nmax = 24; Rest[CoefficientList[Series[Sum[Sum[x^(j k)/(j k), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
%t A318249 nmax = 24; Rest[CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!]
%o A318249 (PARI) a(n) = (n-1)!*numdiv(n); \\ _Michel Marcus_, Aug 22 2018
%Y A318249 Column 1 of A338805.
%Y A318249 Cf. A000005, A028342, A038048, A318250, A338814.
%K A318249 nonn
%O A318249 1,2
%A A318249 _Ilya Gutkovskiy_, Aug 22 2018