cp's OEIS Frontend

A325403 Number of permutations of the multiset of prime factors of 2n whose first part is not 2.

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