A261129 Highest exponent in prime factorization of the swinging factorial (A056040).

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

Amiram Eldar, Table of n, a(n) for n = 2..10000

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

Cf. A000120, A000523, A056040, A263922.

Sequence in context: A334144 A232551 A367006 * A309121 A305871 A089049

Adjacent sequences: A261126 A261127 A261128 * A261130 A261131 A261132

Keyword

nonn

Author

Peter Luschny, Oct 31 2015

Status

approved