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%I #4 Aug 26 2018 20:13:33
%S 0,1,2,3,3,4,4,6,6,5,5,7,6,6,7,10,7,9,8,8,8,7,9,11,9,8,12,9,10,10,11,
%T 15,9,9,10,13,12,10,10,12,13,11,14,10,13,11,15,16,12,12,11,11,16,16,
%U 11,13,12,12,17,14,18,13,14,21,12,12,19,12,13,13,20,18
%N Sum of elements of the multiset spanning an initial interval of positive integers with multiplicities equal to the prime indices of n in weakly decreasing order.
%F a(n) = A056239(A181821(n)).
%e The multiset spanning an initial interval of positive integers with multiplicities equal to the prime indices of 90 in weakly decreasing order is {1,1,1,2,2,3,3,4}, so a(90) = 1+1+1+2+2+3+3+4 = 17.
%t nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t Total/@Array[nrmptn,100]
%Y Row sums of A305936.
%Y Cf. A000041, A000720, A001221, A001222, A056239, A112798, A181821, A182850, A296150, A304464.
%K nonn
%O 1,3
%A _Gus Wiseman_, Aug 23 2018
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