A060737 Number of distinct differences between consecutive divisors of n! (ordered by size).

0, 0, 1, 2, 4, 9, 15, 27, 44, 72, 116, 230, 379, 716, 1154, 1858, 2589, 5014, 7299, 15276, 21901, 33146, 52298, 102918, 136647, 200669, 327572, 432396, 596869, 1220172, 1603092, 3074018, 3752018, 5433507, 8555035, 11952469, 14590378, 30158257, 46318453, 66458379

Offset: 0

Author

Labos Elemer, Apr 25 2001

Keywords

• nonn

Examples

			For n = 4, n! = 24; divisors = {1,2,3,4,6,8,12,24}; differences = {1,1,1,2,2,4,12}, distinct differences = {1,2,4,12}, so a(4) = 4.
		

Crossrefs

Cf. A000142, A060682, A060738, A060742.

Programs

Mathematica

a[n_ ] := Length[Union[Drop[d=Divisors[n! ], 1]-Drop[d, -1]]]
Table[Length[Union[Differences[Divisors[n!]]]],{n,0,40}] (* Harvey P. Dale, Nov 22 2021 *)

PARI

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

Formula

a(n) = A060682(n!).

Extensions

Edited by Dean Hickerson, Jan 22 2002

More terms from Ryan Propper, Mar 22 2006

a(37)-a(39) from Amiram Eldar, Jun 15 2024