OFFSET
2,2
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 version where zero is prepended to the prime indices before taking differences is A287352.
One could argue that row n = 1 is empty, but adding it changes only the offset, with no effect on the data.
LINKS
FORMULA
Row lengths are 1 or A001222(n) - 1 depending on whether n is prime.
EXAMPLE
Triangle begins (showing n, prime indices, differences*):
2: (1) 1
3: (2) 2
4: (1,1) 0
5: (3) 3
6: (1,2) 1
7: (4) 4
8: (1,1,1) 0 0
9: (2,2) 0
10: (1,3) 2
11: (5) 5
12: (1,1,2) 0 1
13: (6) 6
14: (1,4) 3
15: (2,3) 1
16: (1,1,1,1) 0 0 0
For example, the prime indices of 24 are (1,1,1,2), with differences (0,0,1).
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[PrimeQ[n], {PrimePi[n]}, Differences[primeMS[n]]], {n, 2, 30}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Jul 12 2022
STATUS
approved