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%I #15 Jul 29 2023 03:17:15
%S 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,
%T 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,
%U 3,3,2,2,3,3,3,3,4,4,2,4,4,4,3,3,4,4,4
%N Highest exponent in prime factorization of the swinging factorial (A056040).
%C A263922 is a subsequence.
%H Amiram Eldar, <a href="/A261129/b261129.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = A051903(A056040(n)) for n>=2.
%F A000120(floor(n/2)) <= a(n) <= A000523(n), (n>=2).
%p swing := n -> n!/iquo(n,2)!^2:
%p max_exp := n -> max(seq(s[2], s=ifactors(n)[2])):
%p seq(max_exp(swing(n)), n=2..88);
%t a[n_] := Max[FactorInteger[n!/Quotient[n, 2]!^2][[;; , 2]]]; Array[a, 100, 2] (* _Amiram Eldar_, Jul 29 2023 *)
%o (Sage)
%o swing = lambda n: factorial(n)//factorial(n//2)^2
%o max_exp = lambda n: max(e for p, e in n.factor())
%o [max_exp(swing(n)) for n in (2..88)]
%Y Cf. A000120, A000523, A056040, A263922.
%K nonn
%O 2,5
%A _Peter Luschny_, Oct 31 2015
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