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A056606
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Squarefree kernel of lcm(binomial(n,0), ..., binomial(n,n)).
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7
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1, 1, 2, 3, 6, 10, 30, 105, 70, 42, 210, 2310, 2310, 4290, 6006, 15015, 30030, 170170, 510510, 1939938, 1385670, 881790, 9699690, 223092870, 44618574, 17160990, 74364290, 31870410, 223092870, 6469693230, 6469693230, 100280245065
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OFFSET
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0,3
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COMMENTS
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Also the squarefree kernel of the cumulative product of n^n/n!. - Peter Luschny, Dec 21 2019
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LINKS
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FORMULA
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EXAMPLE
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a(7) = 105 because lcm(1, 7, 21, 35) = 105 is already squarefree.
a(0) = 1 because n^n/n! = 1 for the integer n = 0. - Peter Luschny, Dec 21 2019
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MAPLE
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h := n -> mul(k^k/factorial(k), k=0..n):
rad := n -> mul(k, k = numtheory[factorset](n)):
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MATHEMATICA
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Table[Apply[Times, FactorInteger[Product[k^(2 k - 1 - n), {k, n}]][[All, 1]]], {n, 0, 31}] (* or *)
Table[Apply[Times, FactorInteger[Apply[LCM, Range@ n]/n][[All, 1]]], {n, 1, 32}] (* Michael De Vlieger, Jul 14 2017 *)
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PROG
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(Haskell)
(PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
a(n) = rad(lcm(vector(n+1, k, binomial(n, k-1)))); \\ Michel Marcus, Jun 24 2023
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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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