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

1, 2, 4, 18, 48, 480, 1440, 20160, 120960, 1451520, 7257600, 239500800, 958003200, 24908083200, 348713164800, 6538371840000, 41845579776000, 2134124568576000, 12804747411456000, 729870602452992000, 9731608032706560000, 204363768686837760000, 2248001455555215360000, 206816133911079813120000

Offset: 1

Author

Ilya Gutkovskiy, Aug 22 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..450

Crossrefs

Column 1 of A338805.

Cf. A000005, A028342, A038048, A318250, A338814.

Programs

Mathematica

Table[(n - 1)! DivisorSigma[0, n], {n, 1, 24}]
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]!]
nmax = 24; Rest[CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!]

PARI

a(n) = (n-1)!*numdiv(n); \\ Michel Marcus, Aug 22 2018

Formula

E.g.f.: Sum_{k>=1} Sum_{j>=1} x^(j*k)/(j*k).

E.g.f.: -log(Product_{k>=1} (1 - x^k)^(1/k)).

E.g.f.: A(x) = log(B(x)), where B(x) = e.g.f. of A028342.

a(p^k) = (k + 1)*(p^k - 1)!, where p is a prime.