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

1,2

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A008683.

Numerator: A080304, A080306, A034386.

Sequence in context: A249386 A384443 A089026 * A220137 A053815 A194446

Adjacent sequences: A080302 A080303 A080304 * A080306 A080307 A080308

Keyword

nonn,frac

Author

Reinhard Zumkeller, Feb 13 2003

Status

approved