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

0,4

Links

Table of n, a(n) for n=0..39.

Formula

a(n) = A060682(n!).

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000142, A060682, A060738, A060742.

Sequence in context: A080004 A176915 A060742 * A266647 A085683 A330737

Adjacent sequences: A060734 A060735 A060736 * A060738 A060739 A060740

Keyword

nonn

Author

Labos Elemer, Apr 25 2001

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

Status

approved