A357875 - OEIS

A357875

Numbers whose run-sums of prime indices are weakly increasing.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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.

The sequence of runs of a sequence consists of its maximal consecutive constant subsequences when read left-to-right. For example, the runs of (2,2,1,1,1,3,2,2) are (2,2), (1,1,1), (3), (2,2), with sums (4,3,3,4).

LINKS

Table of n, a(n) for n=1..67.

Mathematics Stack Exchange, What is a sequence run? (answered 2011-12-01)

EXAMPLE

The prime indices of 24 are (1,1,1,2), with run-sums (3,2), which are not weakly increasing, so 24 is not in the sequence.

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[100], LessEqual@@Total/@Split[primeMS[#]]&]

CROSSREFS

These partitions are counted by A304405.

These are the indices of rows in A354584 that are weakly increasing.

The complement is A357876.