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A335432
Number of anti-run permutations of the prime indices of Mersenne numbers A000225(n) = 2^n - 1.
4
1, 1, 1, 2, 1, 1, 1, 6, 2, 6, 2, 36, 1, 6, 6, 24, 1, 24, 1, 240, 6, 24, 2, 1800, 6, 6, 6, 720, 6, 1800, 1, 120, 24, 6, 24, 282240, 2, 6, 24, 15120, 2, 5760, 6, 5040, 720, 24, 6, 1451520, 2, 5040, 120, 5040, 6, 1800, 720, 40320, 24, 720, 2, 1117670400, 1, 6, 1800, 5040, 6
OFFSET
1,4
COMMENTS
An anti-run is a sequence with no adjacent equal parts.
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.
LINKS
FORMULA
a(n) = A335452(A000225(n)).
EXAMPLE
The a(1) = 1 through a(10) = 6 permutations:
() (2) (4) (2,3) (11) (2,4,2) (31) (2,3,7) (21,4) (11,2,5)
(3,2) (2,7,3) (4,21) (11,5,2)
(3,2,7) (2,11,5)
(3,7,2) (2,5,11)
(7,2,3) (5,11,2)
(7,3,2) (5,2,11)
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, 0, 30}]
PROG
(PARI) \\ See A335452 for count.
a(n) = {count(factor(2^n-1)[, 2])} \\ Andrew Howroyd, Feb 03 2021
CROSSREFS
The version for factorial numbers is A335407.
Anti-run compositions are A003242.
Anti-run patterns are A005649.
Permutations of prime indices are A008480.
Anti-runs are ranked by A333489.
Separable partitions are ranked by A335433.
Inseparable partitions are ranked by A335448.
Anti-run permutations of prime indices are A335452.
Strict permutations of prime indices are A335489.
Sequence in context: A293902 A300830 A139329 * A229557 A332700 A256268
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 02 2020
EXTENSIONS
Terms a(51) and beyond from Andrew Howroyd, Feb 03 2021
STATUS
approved