A353833 - OEIS

A353833

Numbers whose multiset of prime indices has all equal run-sums.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 40, 41, 43, 47, 49, 53, 59, 61, 63, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 112, 113, 121, 125, 127, 128, 131, 137, 139, 144, 149, 151, 157, 163, 167, 169, 173, 179

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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..61.

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

EXAMPLE

The prime indices of 12 are {1,1,2}, with run-sums (2,2), so 12 is in the sequence.

MATHEMATICA

Select[Range[100], SameQ@@Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]*k]&]

CROSSREFS

For parts instead of run-sums we have A000961, counted by A000005.

For run-lengths instead of run-sums we have A072774, counted by A047966.

These partitions are counted by A304442.

These are the positions of powers of primes in A353832.