A080305 Denominator of n^mu(n), where mu is the Moebius function (A008683).

1, 2, 3, 1, 5, 1, 7, 1, 1, 1, 11, 1, 13, 1, 1, 1, 17, 1, 19, 1, 1, 1, 23, 1, 1, 1, 1, 1, 29, 30, 31, 1, 1, 1, 1, 1, 37, 1, 1, 1, 41, 42, 43, 1, 1, 1, 47, 1, 1, 1, 1, 1, 53, 1, 1, 1, 1, 1, 59, 1, 61, 1, 1, 1, 1, 66, 67, 1, 1, 70, 71, 1, 73, 1, 1, 1, 1, 78, 79, 1, 1, 1, 83, 1, 1, 1, 1, 1, 89, 1, 1, 1, 1

Offset: 1

Author

Reinhard Zumkeller, Feb 13 2003

Keywords

• nonn
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A008683.

Numerator: A080304, A080306, A034386.

Programs

Mathematica

Table[n^MoebiusMu[n],{n,100}]//Denominator (* Harvey P. Dale, Jun 18 2023 *)

PARI

A080305(n) = denominator(n^moebius(n)); \\ Antti Karttunen, Aug 06 2018

Formula

a(n) = if mu(n)<0 then n else 1, where mu is Moebius mu function (A008683).