A351564 a(n) = 1 if all the exponents in the prime factorization of n are distinct, and 0 otherwise.

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

Offset

1

Links

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

Index entries for characteristic functions.

Index entries for sequences computed from exponents in factorization of n.

Formula

a(n) = A008966(A181819(n)).

Example

For n = 4 = 2^2, all the exponents present [2] are distinct, therefore a(4) = 1.
For n = 300 = 2^2 * 3^1 * 5^2, the exponents are [2, 1, 2], thus they are not all distinct, therefore a(300) = 0.

Mathematica

a[n_] := If[UnsameQ @@ FactorInteger[n][[;; , 2]], 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 30 2022 *)

Prog

(PARI) A351564(n) = issquarefree(factorback(apply(e->prime(e), (factor(n)[, 2]))));

Crossrefs

Characteristic function of A130091.

Cf. A008966, A181819, A327498, A327499.

Sequence in context: A142720 A196308 A091862 * A237048 A344880 A167020

Adjacent sequences: A351561 A351562 A351563 * A351565 A351566 A351567

Keyword

nonn

Author

Antti Karttunen, Apr 02 2022

Status

approved