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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 (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 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: A080099 A268040 A127711 * A199238 A181347 A014587 Adjacent sequences:  A069581 A069582 A069583 * A069585 A069586 A069587 KEYWORD easy,nonn AUTHOR Amarnath Murthy, Mar 24 2002 EXTENSIONS Edited by Reinhard Zumkeller, Mar 26 2003 STATUS approved

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Last modified August 5 06:46 EDT 2020. Contains 336209 sequences. (Running on oeis4.)