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

Author

Peter Luschny, Oct 31 2015

Keywords

• nonn

Comments

A263922 is a subsequence.

Links

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

Crossrefs

Cf. A000120, A000523, A056040, A263922.

Programs

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 *)

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)]

Formula

a(n) = A051903(A056040(n)) for n>=2.

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