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

%I A182921 #19 Jun 13 2025 07:45:36
%S A182921 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 A182921 9,11,11,13,11,12,12,14,12,13,12,13,12,15,15,16,13,15,14,16,15,16,14,
%U A182921 16,14,16,16,17,15,16,16,19,15,17,16,17,16,18,17,18,15
%N A182921 Sum of exponents in prime-power factorization of the swinging factorial (A056040) n$ = n!/floor(n/2)!^2; also bigomega(n$).
%H A182921 Amiram Eldar, <a href="/A182921/b182921.txt">Table of n, a(n) for n = 0..10000</a>
%e A182921 16$ = 2*3*3*5*11*13. Thus a(16) = 6.
%p A182921 A056040 := n -> n! / iquo(n,2)!^2;
%p A182921 A182921 := n -> numtheory[bigomega](A056040(n)): seq(A182921(i), i=0..70);
%t A182921 a[n_] := PrimeOmega[n!/Quotient[n, 2]!^2];
%t A182921 Table[a[n], {n, 0, 64}] (* _Jean-François Alcover_, Jun 18 2019 *)
%o A182921 (PARI) a(n) = bigomega(n! / (n\2)!^2); \\ _Amiram Eldar_, Jun 13 2025
%Y A182921 Cf. A001222, A022559, A056040.
%K A182921 nonn
%O A182921 0,4
%A A182921 _Peter Luschny_, Mar 14 2011