OFFSET
1,3
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 augmented differences aug(q) of a (usually weakly decreasing) sequence q of length k are given by aug(q)_i = q_i - q_{i+1} + 1 if i < k and aug(q)_k = q_k. For example, we have aug(6,5,5,3,3,3) = (2,1,3,1,1,3).
LINKS
EXAMPLE
The reversed prime indices of 825 are (5,3,3,2), with augmented differences (3,1,2,2), so a(825) = 3.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
aug[y_]:=Table[If[i<Length[y], y[[i]]-y[[i+1]]+1, y[[i]]], {i, Length[y]}];
Table[If[n==1, 0, Max@@aug[Reverse[primeMS[n]]]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 14 2022
STATUS
approved