|
%I #10 Dec 07 2021 11:08:14
%S 0,0,1,0,1,1,1,0,2,1,1,1,1,1,4,0,1,3,1,1,4,1,1,1,2,1,3,1,1,6,1,0,4,1,
%T 4,4,1,1,4,1,1,6,1,1,9,1,1,1,2,3,4,1,1,6,4,1,4,1,1,8,1,1,9,0,4,6,1,1,
%U 4,6,1,5,1,1,9,1,4,6,1,1,4,1,1,8,4,1,4,1,1,18,4,1,4,1,4,1,1,3,9,4,1,6,1,1,18
%N Number of permutations of the multiset of prime factors of 2n whose first part is not 2.
%H Antti Karttunen, <a href="/A325403/b325403.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = A008480(2n) - A008480(n) = A325392(2n).
%e The a(60) = 8 permutations of {2,2,2,3,5} whose first part is not 2:
%e 3 2 2 2 5
%e 3 2 2 5 2
%e 3 2 5 2 2
%e 3 5 2 2 2
%e 5 2 2 2 3
%e 5 2 2 3 2
%e 5 2 3 2 2
%e 5 3 2 2 2
%t Table[Length[Select[Permutations[Flatten[Table@@@FactorInteger[2*n]]],First[#]!=2&]],{n,100}]
%o (PARI)
%o A008480(n) = {my(sig=factor(n)[, 2]); vecsum(sig)!/factorback(apply(k->k!, sig))}; \\ After code in A008480
%o A325403(n) = (A008480(n+n)-A008480(n)); \\ _Antti Karttunen_, Dec 06 2021
%Y Cf. A008480, A056239, A112798, A325327, A325362, A325364, A325367, A325390, A325392, A325407.
%K nonn
%O 1,9
%A _Gus Wiseman_, May 02 2019
%E Data section extended up to 105 terms by _Antti Karttunen_, Dec 06 2021
|
