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

0,9

Links

Table of n, a(n) for n=0..41.

Formula

a(n) = A060763(n!).

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A262192 A280308 A289121 * A090651 A242497 A062201

Adjacent sequences: A060735 A060736 A060737 * A060739 A060740 A060741

Keyword

nonn

Author

Labos Elemer, Apr 25 2001

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

Status

approved