OFFSET
1,5
COMMENTS
A prime index of n is a number m such that prime(m) divides n.
Also the number of squares in the Young diagram of the integer partition with Heinz number n after the first row or the first column, whichever is smaller, is removed. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
LINKS
EXAMPLE
88 has 4 prime indices {1,1,1,5} with sum 8 and maximum 5, so a(88) = 8 - min(4,5) = 4.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[n==1, 0, Total[primeMS[n]]-Min[Length[primeMS[n]], Max[primeMS[n]]]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 12 2019
STATUS
approved