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A336104
Number of permutations of the prime indices of A000225(n) = 2^n - 1 with at least one non-singleton run.
1
0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 96, 0, 120, 6, 0, 0, 720, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 322560, 0, 0, 0, 5040, 0, 4320, 0, 0, 0, 0, 0, 362880, 0, 0
OFFSET
1,6
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
FORMULA
a(n) = A336107(2^n - 1).
a(n) = A336105(n) - A335432(n).
EXAMPLE
The a(21) = 6 permutations of {4, 4, 31, 68}:
(4,4,31,68)
(4,4,68,31)
(31,4,4,68)
(31,68,4,4)
(68,4,4,31)
(68,31,4,4)
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Select[Permutations[primeMS[2^n-1]], MatchQ[#, {___, x_, x_, ___}]&]], {n, 30}]
CROSSREFS
A335432 is the anti-run version.
A335459 is the version for factorial numbers.
A336105 counts all permutations of this multiset.
A336107 is not restricted to predecessors of powers of 2.
A003242 counts anti-run compositions.
A005649 counts anti-run patterns.
A008480 counts permutations of prime indices.
A325534 counts separable partitions, ranked by A335433.
A325535 counts inseparable partitions, ranked by A335448.
A333489 ranks anti-run compositions.
A335433 lists numbers whose prime indices have an anti-run permutation.
A335448 lists numbers whose prime indices have no anti-run permutation.
A335452 counts anti-run permutations of prime indices.
A335489 counts strict permutations of prime indices.
Sequence in context: A123298 A189877 A189868 * A110981 A019261 A019222
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 03 2020
STATUS
approved