A069585 a(n) = n - largest prime 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, 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, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0

Offset: 1

Author

Amarnath Murthy, Mar 24 2002

Keywords

• easy
• nonn

Comments

This sequence considers "prime powers" to be A025475 rather than A000961.

a(8)=a(9)=0. With Mihăilescu's proof of Catalan's conjecture (see A001597) there can be no further occurrence of consecutive zeros. - Robert Munafo, May 10 2024

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A031218, A069584.

Programs

Mathematica

nn = 10^4; s = {1}~Join~Select[Union@ Flatten@ Table[a^2*b^3, {b, Surd[nn, 3]}, {a, Sqrt[nn/b^3]}], PrimePowerQ]; Table[n - TakeWhile[s, # <= n &][[-1]], {n, nn}] (* Michael De Vlieger, May 11 2024 *)

Formula

a(n) = n - A167185(n). - Michel Marcus, May 10 2024

Extensions

Revised by Robert Munafo and Sean A. Irvine, May 10 2024