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A056044
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Let k be the largest number such that k^2 divides n! and let m be the largest number such that m!^2 divides n!; a(n) = k/m!.
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3
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1, 1, 1, 1, 1, 2, 2, 1, 3, 1, 1, 2, 2, 2, 6, 3, 3, 2, 2, 2, 2, 2, 2, 2, 10, 10, 30, 2, 2, 12, 12, 3, 3, 6, 30, 10, 10, 10, 30, 6, 6, 2, 2, 2, 30, 60, 60, 30, 210, 42, 42, 42, 42, 1, 1, 2, 2, 4, 4, 4, 4, 4, 84, 21, 21, 14, 14, 14, 42, 6, 6, 2, 2, 2, 10, 10, 70, 140, 140, 14, 126, 3, 3, 6, 30
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OFFSET
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1,6
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LINKS
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FORMULA
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EXAMPLE
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For n = 11, 11! = 6! * 6! * 77, so A000188(11!) = A056038(11) = 6! and a(11) = 6!/6! = 1.
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MATHEMATICA
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f[p_, e_] := p^Floor[e/2]; b[1] = 1; b[n_] := Times @@ f @@@ FactorInteger[n!];
c[n_] := Module[{k = 1}, NestWhile[#/(++k)^2 &, n!, IntegerQ]; (k-1)!];
a[n_] := b[n] / c[n]; Array[a, 100] (* Amiram Eldar, May 24 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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