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

1,4

Links

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A034699, A088387.

Sequence in context: A307907 A362333 A371148 * A070013 A070014 A051903

Adjacent sequences: A088385 A088386 A088387 * A088389 A088390 A088391

Keyword

nonn

Author

Reinhard Zumkeller, Sep 28 2003

Status

approved