OFFSET
0,4
LINKS
Daniel Berend and J. E. Harmse, Gaps between consecutive divisors of factorials, Ann. Inst. Fourier, 43 (3) (1993), 569-583.
FORMULA
a(n) = A060741(n!/2) for n >= 2. - Amiram Eldar, Jun 15 2024
EXAMPLE
For n = 5, n! = 120; divisors = {1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}; differences = {1,1,1,1,1,2,2,2,3,5,4,6,10,20,60}; intersection = {1,2,3,4,5,6,10,20,60}, so a(5) = 9.
MAPLE
f:= proc(n) local D, L;
D:= numtheory:-divisors(n!);
L:= sort(convert(D, list));
nops(convert(L[2..-1]-L[1..-2], set) intersect D);
end proc:
map(f, [$0..34]); # Robert Israel, Jul 03 2017
MATHEMATICA
a[n_ ] := Length[Intersection[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
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 23 2001
EXTENSIONS
Edited by Dean Hickerson, Jan 22 2002
One more term from Robert G. Wilson v, Jan 29 2002
a(33)-a(35) from Robert Israel, Jul 03 2017
a(36)-a(40) from Amiram Eldar, Jun 15 2024
STATUS
approved