A095997 Number of divisors of n! that are coprime to n.

1, 1, 2, 2, 8, 2, 30, 12, 32, 10, 270, 12, 792, 72, 144, 336, 5376, 96, 14688, 432, 1520, 1600, 96000, 960, 48576, 7392, 48384, 7056, 917280, 720, 2332800, 172800, 122880, 122880, 304128, 31104, 19595520, 559872, 1119744, 262656, 102435840, 46080, 258048000, 3225600, 3386880

Offset

1,3

Comments

a(p_i) < a(p_j) for i<j.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Mathematica

f[n_] := Length[ Select[ Divisors[n! ], GCD[ #, n] == 1 &]]; Table[ f[n], {n, 33}]

Prog

(PARI) a(n)={if(n<=2, 1, numdiv(Mat(select(f->n%f[1], Col(factor(n!))))))} \\ Andrew Howroyd, Nov 05 2019

Crossrefs

Cf. A000142, A027423.

Sequence in context: A363418 A245497 A086328 * A274139 A283995 A056189

Adjacent sequences: A095994 A095995 A095996 * A095998 A095999 A096000

Keyword

nonn

Author

Robert G. Wilson v, Jul 19 2004, based on a suggestion from Leroy Quet, Jun 18 2004

Extensions

Terms a(34) and beyond from Andrew Howroyd, Nov 05 2019

Status

approved