

A060737


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


2



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
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OFFSET

0,4


LINKS

Table of n, a(n) for n=0..36.


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 *)


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


STATUS

approved



