cp's OEIS Frontend

A382774 Number of ways to permute the prime indices of n! so that the run-lengths are all different.

%I A382774 #8 Apr 10 2025 23:22:43
%S A382774 1,1,1,0,2,0,6,0,0,0,96,0
%N A382774 Number of ways to permute the prime indices of n! so that the run-lengths are all different.
%C A382774 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, sum A056239.
%F A382774 a(n) = A382771(n!).
%e A382774 The prime indices of 24 are {1,1,1,2}, with permutations (1,1,1,2) and (2,1,1,1), so a(4) = 2.
%t A382774 Table[Length[Select[Permutations[prix[n!]],UnsameQ@@Length/@Split[#]&]],{n,0,6}]
%Y A382774 For anti-run permutations we have A335407, see also A335125, A382858.
%Y A382774 This is the restriction of A382771 to the factorials A000142, equal A382857.
%Y A382774 A022559 counts prime indices of n!, sum A081401.
%Y A382774 A044813 lists numbers whose binary expansion has distinct run-lengths, equal A140690.
%Y A382774 A056239 adds up prime indices, row sums of A112798.
%Y A382774 A098859 counts partitions with distinct multiplicities, ordered A242882.
%Y A382774 A239455 counts Look-and-Say partitions, ranks A351294, conjugate A381432.
%Y A382774 A328592 lists numbers whose binary form has distinct runs of ones, equal A164707.
%Y A382774 A329738 counts compositions with equal run-lengths, ranks A353744.
%Y A382774 A329739 counts compositions with distinct run-lengths, ranks A351596.
%Y A382774 A351293 counts non-Look-and-Say partitions, ranks A351295, conjugate A381433.
%Y A382774 Cf. A000720, A001221, A001222, A003242, A048767, A130091, A181821, A351013, A351202, A360015, A382773, A382879.
%K A382774 nonn,more
%O A382774 0,5
%A A382774 _Gus Wiseman_, Apr 09 2025