A088388 Exponent of the largest prime power factor of n, a(1)=0.

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 4, 2, 2, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 2, 6, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 5, 1, 2, 1, 2, 1, 1

Offset: 1

Author

Reinhard Zumkeller, Sep 28 2003

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A034699, A088387.

Programs

Mathematica

a[n_] := If[n==1, 0, MaximalBy[FactorInteger[n], #[[1]]^#[[2]]&][[1, 2]]];
Array[a, 100] (* Jean-François Alcover, Dec 03 2021 *)

PARI

A088388(n) = if(1==n,0,my(f=factor(n)); isprimepower(vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2])))); \\ Antti Karttunen, Jul 22 2018

Python

from sympy import factorint
def A088388(n): return max(((p**e,e) for p, e in factorint(n).items()), default=(0,0))[1] # Chai Wah Wu, Apr 17 2023

Formula

A034699(n) = A088387(n)^a(n).