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A353862 Greatest run-sum of the prime indices of n.

%I A353862 #6 May 25 2022 09:12:43
%S A353862 0,1,2,2,3,2,4,3,4,3,5,2,6,4,3,4,7,4,8,3,4,5,9,3,6,6,6,4,10,3,11,5,5,
%T A353862 7,4,4,12,8,6,3,13,4,14,5,4,9,15,4,8,6,7,6,16,6,5,4,8,10,17,3,18,11,4,
%U A353862 6,6,5,19,7,9,4,20,4,21,12,6,8,5,6,22,4,8
%N A353862 Greatest run-sum of the prime indices of n.
%C A353862 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.
%C A353862 A run-sum of a sequence is the sum of any maximal consecutive constant subsequence.
%e A353862 The prime indices of 72 are {1,1,1,2,2}, with run-sums {3,4}, so a(72) = 4.
%t A353862 Table[Max@@Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k],{n,100}]
%Y A353862 Positions of first appearances are A008578.
%Y A353862 For binary expansion we have A038374, least A144790.
%Y A353862 For run-lengths instead of run-sums we have A051903.
%Y A353862 Distinct run-sums are counted by A353835, weak A353861.
%Y A353862 The least run-sum is given by A353931.
%Y A353862 A001222 counts prime factors, distinct A001221.
%Y A353862 A005811 counts runs in binary expansion.
%Y A353862 A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A353862 A124010 gives prime signature, sorted A118914.
%Y A353862 A300273 ranks collapsible partitions, counted by A275870.
%Y A353862 A304442 counts partitions with all equal run-sums, compositions A353851.
%Y A353862 A353832 represents the operation of taking run-sums of a partition.
%Y A353862 A353833 ranks partitions with all equal run sums, nonprime A353834.
%Y A353862 A353838 ranks partitions with all distinct run-sums, counted by A353837.
%Y A353862 A353840-A353846 pertain to partition run-sum trajectory.
%Y A353862 Cf. A067340, A073093, A181819, A182857, A316413, A353836, A353839, A353848, A353852, A353866.
%K A353862 nonn
%O A353862 1,3
%A A353862 _Gus Wiseman_, May 23 2022