A307907 - OEIS

A307907

a(n) is the greatest k such that p^k <= n for any prime factor p of n.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

LINKS

Table of n, a(n) for n=2..88.

Rémy Sigrist, Colored scatterplot of the ordinal transform of n -> a(n^5) - 5*a(n) for n = 2..100000

FORMULA

a(n) = floor(log(n)/log(A006530(n))).

a(p^k) = k for any prime number p and any k > 0.

0 <= a(n^k) - k*a(n) < k for any n > 1 and any k > 0.

a(n) = 1 iff n belongs to A064052.

a(n) > 1 iff n belongs to A048098.