A182921 Sum of exponents in prime-power factorization of the swinging factorial (A056040) n$ = n!/floor(n/2)!^2; also bigomega(n$).

0, 0, 1, 2, 2, 3, 3, 4, 3, 5, 5, 6, 5, 6, 6, 8, 6, 7, 6, 7, 6, 8, 8, 9, 7, 9, 9, 12, 11, 12, 11, 12, 9, 11, 11, 13, 11, 12, 12, 14, 12, 13, 12, 13, 12, 15, 15, 16, 13, 15, 14, 16, 15, 16, 14, 16, 14, 16, 16, 17, 15, 16, 16, 19, 15, 17, 16, 17, 16, 18, 17, 18, 15

Offset: 0

Author

Peter Luschny, Mar 14 2011

Keywords

• nonn

Examples

			16$ = 2*3*3*5*11*13. Thus a(16) = 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001222, A022559, A056040.

Programs

Maple

A056040 := n -> n! / iquo(n,2)!^2;
A182921 := n -> numtheory[bigomega](A056040(n)): seq(A182921(i), i=0..70);

Mathematica

a[n_] := PrimeOmega[n!/Quotient[n, 2]!^2];
Table[a[n], {n, 0, 64}] (* Jean-François Alcover, Jun 18 2019 *)

PARI

a(n) = bigomega(n! / (n\2)!^2); \\ Amiram Eldar, Jun 13 2025