A374706 Sum of minima of the maximal strictly increasing runs in the weakly increasing prime indices of n.

0, 1, 2, 2, 3, 1, 4, 3, 4, 1, 5, 2, 6, 1, 2, 4, 7, 3, 8, 2, 2, 1, 9, 3, 6, 1, 6, 2, 10, 1, 11, 5, 2, 1, 3, 4, 12, 1, 2, 3, 13, 1, 14, 2, 4, 1, 15, 4, 8, 4, 2, 2, 16, 5, 3, 3, 2, 1, 17, 2, 18, 1, 4, 6, 3, 1, 19, 2, 2, 1, 20, 5, 21, 1, 5, 2, 4, 1, 22, 4, 8, 1

Offset: 1

Author

Gus Wiseman, Aug 04 2024

Keywords

• nonn

Comments

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.

Examples

			The prime indices of 540 are {1,1,2,2,2,3}, with strictly increasing runs ({1},{1,2},{2},{2,3}), with minima (1,1,2,2), summing to a(540) = 6.
		

Links

• Gus Wiseman, Sequences counting and ranking compositions by their leaders (for six types of runs).

Crossrefs

For leaders of constant runs we have A066328.

A version for compositions is A374684, row-sums of A374683 (length A124768).

Row-sums of A375128.

For length instead of sum we have A375136.

A055887 counts sequences of partitions with total sum n.

A112798 lists prime indices:

- length A001222, distinct A001221

- leader A055396

- sum A056239

- reverse A296150

Cf. A034296, A141199, A189076, A218482, A279790, A333213, A358836, A374634, A374700, A374758, A375133.

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Total[First/@Split[prix[n],Less]],{n,100}]