A211392 The number of divisors d of n! such that the symmetric group on n letters contains no elements of order d.

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

Alois P. Heinz, Table of n, a(n) for n = 1..1000

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

Cf. A000005, A009490, A027423, A211391.

Sequence in context: A291949 A001979 A209970 * A309777 A128516 A022569

Adjacent sequences: A211389 A211390 A211391 * A211393 A211394 A211395

Keyword

nonn

Author

Alexander Gruber, Feb 07 2013

Extensions

More terms from Alois P. Heinz, Feb 11 2013

Status

approved