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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, 30158257, 46318453, 66458379
OFFSET
0,4
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
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