A132350 If n > 1 is a k-th power with k >= 2 then a(n) = 0, otherwise a(n) = 1.

1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = 1 - A075802(n) for n >= 2. - R. J. Mathar, Nov 12 2007

Given the Möbius function mu(n) = A008683(n), a(n) = abs(mu(n)) unless n is in A303946. - Alonso del Arte, May 28 2018

Example

a(4) = 0 because 4 = 2^2.
a(8) = 0 because 8 = 2^3.
a(12) = 1 because 12 is not a perfect power (though it is divisible by a perfect power).

Mathematica

Table[Boole[GCD@@FactorInteger[n][[All, 2]] == 1], {n, 100}] (* Alonso del Arte, May 28 2018 *)

Prog

(PARI) (a(n)=!ispower(n)); (r(nMax) = for(j=1, nMax, print1(!ispower(j)", "))); r(100)
(Haskell)
a132350 1 = 1
a132350 n = 1 - a075802 n  -- Reinhard Zumkeller, Jun 14 2013

Crossrefs

Cf. A132349, A132351, A132352, A075802, A001597.

Sequence in context: A167021 A267687 A304653 * A076213 A368907 A120525

Adjacent sequences: A132347 A132348 A132349 * A132351 A132352 A132353

Keyword

nonn

Author

N. J. A. Sloane, Nov 11 2007

Extensions

Edited by M. F. Hasler, Jun 01 2018

Status

approved