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

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.

A001222 counts prime factors, distinct A001221.

A056239 adds up prime indices, row sums of A112798.

Cf. A047966, A118914, A181819, A239312, A275870, A300273, A304442, A325249, A353743-A354912.

Sequence in context: A351831 A328617 A230308 * A064598 A366187 A364354

Adjacent sequences: A357872 A357873 A357874 * A357876 A357877 A357878

Keyword

nonn

Author

Gus Wiseman, Oct 18 2022

Status

approved