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%I #12 Jun 18 2019 03:18:25
%S 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,
%T 9,11,11,13,11,12,12,14,12,13,12,13,12,15,15,16,13,15,14,16,15,16,14,
%U 16,14,16,16,17,15,16,16,19,15
%N Sum of exponents in prime-power factorization of the swinging factorial (A056040) n$ = n!/floor(n/2)!^2; also bigomega(n$).
%e 16$ = 2.3.3.5.11.13. Thus a(16) = 6.
%p A056040 := n -> n! / iquo(n,2)!^2;
%p A182921 := n -> numtheory[bigomega](A056040(n)): seq(A182921(i), i=0..70);
%t a[n_] := PrimeOmega[n!/Quotient[n, 2]!^2];
%t Table[a[n], {n, 0, 64}] (* _Jean-François Alcover_, Jun 18 2019 *)
%Y Cf. A001222, A022559, A056040.
%K nonn
%O 0,4
%A _Peter Luschny_, Mar 14 2011