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A261129 Highest exponent in prime factorization of the swinging factorial (A056040). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,5

COMMENTS

A000120(floor(n/2)) <= a(n) <= A000523(n), (n>=2).

A263922 is a subsequence.

LINKS

Table of n, a(n) for n=2..88.

FORMULA

a(n) = A051903(A056040(n)) for 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);

PROG

(Sage)

swing = lambda n: factorial(n)//factorial(n//2)^2

max_exp = lambda n: max([p[1] for p in list(n.factor())])

print [max_exp(swing(n)) for n in (2..88)]

CROSSREFS

Cf. A000120, A000523, A056040, A263922.

Sequence in context: A023568 A081753 A232551 * A305871 A089049 A275235

Adjacent sequences:  A261126 A261127 A261128 * A261130 A261131 A261132

KEYWORD

nonn

AUTHOR

Peter Luschny, Oct 31 2015

STATUS

approved

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Last modified July 15 16:29 EDT 2019. Contains 325049 sequences. (Running on oeis4.)