A069584 - OEIS

A069584

a(n) = n - largest perfect power <= n.

0, 1, 2, 0, 1, 2, 3, 0, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 0, 1, 2, 3, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

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

OFFSET

1,3

COMMENTS

a(n) = 0 if n = m^p that is if n is a full power (square, cube etc.).

As Catalan's conjecture is now proved, n=8=2^3, n+1=9=3^2 is the only solution for a(n+1) = a(n) = 0.

LINKS

Table of n, a(n) for n=1..95.

Eric Weisstein's World of Mathematics, Catalan's conjecture

PROG

(PARI) a(n) = {m = n; while(!ispower(m), m--; if (m==0, return (n-1))); n-m; } \\ Michel Marcus, Nov 04 2015

CROSSREFS