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A318283 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. 58
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, 15, 9, 9, 10, 13, 12, 10, 10, 12, 13, 11, 14, 10, 13, 11, 15, 16, 12, 12, 11, 11, 16, 16, 11, 13, 12, 12, 17, 14, 18, 13, 14, 21, 12, 12, 19, 12, 13, 13, 20, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = A056239(A181821(n)).
EXAMPLE
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.
MATHEMATICA
nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Total/@Array[nrmptn, 100]
CROSSREFS
Row sums of A305936.
Sequence in context: A226107 A365659 A344870 * A105677 A230476 A103297
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 23 2018
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)