A351202 - OEIS

%I #8 Feb 15 2022 21:59:59

%S 1,1,1,1,1,2,1,1,1,2,1,2,1,2,2,1,1,2,1,2,2,2,1,4,1,2,1,2,1,6,1,1,2,2,

%T 2,2,1,2,2,4,1,6,1,2,2,2,1,4,1,2,2,2,1,4,2,4,2,2,1,6,1,2,2,1,2,6,1,2,

%U 2,6,1,4,1,2,2,2,2,6,1,4,1,2,1,6,2,2,2

%N Number of permutations of the multiset of prime factors of n (or ordered prime factorizations of n) with all distinct runs.

%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/q/87559">What is a sequence run? (answered 2011-12-01)</a>

%e The a(36) = 2 permutations are (1,1,2,2), (2,2,1,1). Missing are: (1,2,1,2), (1,2,2,1), (2,1,1,2), (2,1,2,1). Here we use prime indices instead of factors.

%t Table[Length[Select[Permutations[Join@@ ConstantArray@@@FactorInteger[n]],UnsameQ@@Split[#]&]],{n,100}]

%Y The maximum number of possible permutations is A008480.

%Y Positions less than A008480 are A351201.

%Y A005811 counts runs in binary expansion.

%Y A044813 lists numbers whose binary expansion has distinct run-lengths.

%Y A056239 adds up prime indices, row sums of A112798.

%Y A098859 counts partitions with distinct multiplicities, ordered A242882.

%Y A283353 counts normal multisets with a permutation without distinct runs.

%Y A297770 counts distinct runs in binary expansion.

%Y A351014 counts distinct runs in standard compositions, firsts A351015.

%Y A351204 = partitions whose perms. have distinct runs, complement A351203.

%Y Counting words with all distinct runs:

%Y - A351013 = compositions, for run-lengths A329739, ranked by A351290.

%Y - A351016 = binary words, for run-lengths A351017.

%Y - A351018 = binary expansions, for run-lengths A032020, ranked by A175413.

%Y - A351200 = patterns, for run-lengths A351292.

%Y Cf. A001055, A001221, A001222, A003242, A061395, A116608, A238130 or A238279, A328592, A351291.

%K nonn

%O 1,6

%A _Gus Wiseman_, Feb 13 2022