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A211392
The number of divisors d of n! such that the symmetric group on n letters contains no elements of order d.
2
0, 0, 1, 4, 10, 24, 51, 85, 146, 254, 520, 769, 1557, 2561, 3997, 5333, 10705, 14633, 29315, 40970, 60722, 95912, 191902, 242769, 339909, 532088, 677224, 917112, 1834373, 2332596, 4665375, 5529352, 7864049, 12164824, 16422587, 19595164, 39190653, 60465758
OFFSET
1,4
LINKS
FORMULA
a(n) = A000005(n!) - A009490(n).
MAPLE
b:= proc(n, i) option remember; local p;
p:= `if`(i<1, 1, ithprime(i));
`if`(n=0 or i<1, 1, b(n, i-1)+
add(b(n-p^j, i-1), j=1..ilog[p](n)))
end:
a:= n-> numtheory[tau](n!) -b(n, numtheory[pi](n)):
seq(a(n), n=1..100); # Alois P. Heinz, Feb 15 2013
MATHEMATICA
b[n_, i_] := b[n, i] = Module[{p}, p = If[i<1, 1, Prime[i]]; If[n==0 || i<1, 1, b[n, i-1] + Sum[b[n-p^j, i-1], {j, 1, Floor@Log[p, n]}]]];
a[n_] := DivisorSigma[0, n!] - b[n, PrimePi[n]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 24 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Gruber, Feb 07 2013
EXTENSIONS
More terms from Alois P. Heinz, Feb 11 2013
STATUS
approved