A060738 Number of distinct differences between consecutive divisors (ordered by increasing magnitude) of n! which are not also divisors of n!.

0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 5, 12, 51, 92, 225, 340, 573, 1325, 2334, 6024, 8724, 13130, 21601, 46169, 67213, 106427, 178014, 242104, 338499, 727248, 988029, 1924615, 2426894, 3592164, 5817845, 8360196, 10396523, 21941765, 33649653, 48804040, 61413482, 124029358

Offset: 0

Author

Labos Elemer, Apr 25 2001

Keywords

• nonn

Examples

			For n up to 7 all divisor differences of n! are also divisors of n!.
For n = 8, there are 3 divisor differences of 8! = 40320 which are not divisors of 8!, namely 27, 54 and 108.
		

Crossrefs

Cf. A000142, A027423, A060737, A060742, A060763.

Programs

Mathematica

a[n_ ] := Length[Complement[Drop[d=Divisors[n! ], 1]-Drop[d, -1], d]]

PARI

a(n) = {my(v = List(), f = n!, d1 = 1, del); fordiv(f, d, if(d > 1, del = d - d1; if(f % del, listput(v, del)); d1 = d)); #Set(v);} \\ Amiram Eldar, Jun 15 2024

Formula

a(n) = A060763(n!).

Extensions

Edited by Dean Hickerson, Jan 22 2002

More terms from Sean A. Irvine, Dec 21 2022

a(41) from Amiram Eldar, Jun 15 2024