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A261129
Highest exponent in prime factorization of the swinging factorial (A056040).
1
1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 4, 4, 2, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 4, 4, 2, 2, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 4, 4, 5, 5, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 4, 4, 2, 4, 4, 4, 3, 3, 4, 4, 4
OFFSET
2,5
COMMENTS
A263922 is a subsequence.
LINKS
FORMULA
a(n) = A051903(A056040(n)) for n>=2.
A000120(floor(n/2)) <= a(n) <= A000523(n), (n>=2).
MAPLE
swing := n -> n!/iquo(n, 2)!^2:
max_exp := n -> max(seq(s[2], s=ifactors(n)[2])):
seq(max_exp(swing(n)), n=2..88);
MATHEMATICA
a[n_] := Max[FactorInteger[n!/Quotient[n, 2]!^2][[;; , 2]]]; Array[a, 100, 2] (* Amiram Eldar, Jul 29 2023 *)
PROG
(Sage)
swing = lambda n: factorial(n)//factorial(n//2)^2
max_exp = lambda n: max(e for p, e in n.factor())
[max_exp(swing(n)) for n in (2..88)]
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Oct 31 2015
STATUS
approved