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.

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

Offset

1,3

Links

Table of n, a(n) for n=1..72.

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.

Cf. A000041, A000720, A001221, A001222, A056239, A112798, A181821, A182850, A296150, A304464.

Sequence in context: A226107 A365659 A344870 * A105677 A230476 A103297

Adjacent sequences: A318280 A318281 A318282 * A318284 A318285 A318286

Keyword

nonn

Author

Gus Wiseman, Aug 23 2018

Status

approved