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 A060742 Number of divisors of n! which are also differences between consecutive divisors of n! (ordered by size). 6
 0, 0, 1, 2, 4, 9, 15, 27, 41, 68, 111, 218, 328, 624, 929, 1518, 2016, 3689, 4965, 9252, 13177, 20016, 30697, 56749, 69434, 94242, 149558, 190292, 258370, 492924, 615063, 1149403, 1325124, 1841343, 2737190, 3592273 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS D. Berend et al., Gaps between consecutive divisors of factorials, Ann. Inst. Fourier, 43 (3) (1993), 569-583. 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]] CROSSREFS Cf. A000142, A027423, A060737, A060738, A060741. Sequence in context: A157254 A080004 A176915 * A060737 A266647 A085683 Adjacent sequences: A060739 A060740 A060741 * A060743 A060744 A060745 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 STATUS approved

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Last modified December 9 14:59 EST 2022. Contains 358700 sequences. (Running on oeis4.)