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A069584
a(n) = n - largest perfect power <= n.
2
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
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
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
Cf. A001597, a(n)=n-A081676(n).
Sequence in context: A268040 A127711 A336937 * A069585 A199238 A346698
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Mar 24 2002
EXTENSIONS
Edited by Reinhard Zumkeller, Mar 26 2003
STATUS
approved