A025477 a(n) = exponent of the n-th nontrivial prime power A025475(n).

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

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A001222, A025475, A051903.

Programs

Mathematica

With[{nn = 2^20}, {0}~Join~Map[FactorInteger[#][[1, -1]] &, Select[Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], PrimePowerQ] ] ] (* Michael De Vlieger, Oct 23 2023 *)

Formula

a(n) = A051903(A025475(n)) = A001222(A025475(n)). - Reinhard Zumkeller, Mar 10 2003

Extensions

Edited by N. J. A. Sloane, Jan 17 2009 at the suggestion of R. J. Mathar

Name edited by Michael De Vlieger, Oct 23 2023