|
|
A318249
|
|
a(n) = (n - 1)! * d(n), where d(n) = number of divisors of n (A000005).
|
|
11
|
|
|
1, 2, 4, 18, 48, 480, 1440, 20160, 120960, 1451520, 7257600, 239500800, 958003200, 24908083200, 348713164800, 6538371840000, 41845579776000, 2134124568576000, 12804747411456000, 729870602452992000, 9731608032706560000, 204363768686837760000, 2248001455555215360000, 206816133911079813120000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
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.
|
|
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]!]
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|