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A325403 Number of permutations of the multiset of prime factors of 2n whose first part is not 2. 2
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
LINKS
FORMULA
a(n) = A008480(2n) - A008480(n) = A325392(2n).
EXAMPLE
The a(60) = 8 permutations of {2,2,2,3,5} whose first part is not 2:
3 2 2 2 5
3 2 2 5 2
3 2 5 2 2
3 5 2 2 2
5 2 2 2 3
5 2 2 3 2
5 2 3 2 2
5 3 2 2 2
MATHEMATICA
Table[Length[Select[Permutations[Flatten[Table@@@FactorInteger[2*n]]], First[#]!=2&]], {n, 100}]
PROG
(PARI)
A008480(n) = {my(sig=factor(n)[, 2]); vecsum(sig)!/factorback(apply(k->k!, sig))}; \\ After code in A008480
A325403(n) = (A008480(n+n)-A008480(n)); \\ _Antti Karttunen_, Dec 06 2021
CROSSREFS
Sequence in context: A218220 A247487 A010248 * A132068 A173441 A326851
KEYWORD
nonn
AUTHOR
_Gus Wiseman_, May 02 2019
EXTENSIONS
Data section extended up to 105 terms by _Antti Karttunen_, Dec 06 2021
STATUS
approved

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Last modified March 2 02:30 EST 2024. Contains 370447 sequences. (Running on oeis4.)