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A060742
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Number of divisors of n! which are also differences between consecutive divisors of n! (ordered by size).
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6
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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, 4193855, 8216492, 12668800, 17654339, 20368544
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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a[n_ ] := Length[Intersection[Drop[d=Divisors[n! ], 1]-Drop[d, -1], d]]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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