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.
Every sequence can be uniquely split into a sequence of non-overlapping runs. 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).
EXAMPLE
Triangle begins:
.
1
2
2
3
1 2
4
3
4
1 3
5
2 2
6
1 4
2 3
For example, the prime indices of 630 are {1,2,2,3,4}, so row 630 is (1,4,3,4).
MATHEMATICA
Table[Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>PrimePi[p]*k], {n, 30}]
CROSSREFS
Positions of first appearances are A308495 plus 1.
Classes:
- singleton rows: A000961
Statistics:
- row lengths: A001221
- row sums: A056239
- row products: A304117
- row ranks (as partitions): A353832
- row image sizes: A353835
- row maxima: A353862
- row minima: A353931
A001222 counts prime factors with multiplicity.
A353861 counts distinct sums of partial runs of prime indices.
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Jun 17 2022
STATUS
approved