A353800 a(n) = 1 if n is a power of prime with an even exponent, otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100489

Index entries for characteristic functions

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A010055(n) - A353817(n).

a(n) >= A302048(n).

Example

a(1) = 1 because 1 = p^0 for any prime p, and 0 is an even number.

Mathematica

a[n_] := If[n == 1 || (Length[(f = FactorInteger[n])] == 1 && EvenQ[f[[1, 2]]]), 1, 0]; Array[a, 100] (* Amiram Eldar, May 15 2022 *)

Prog

(PARI) A353800(n) = ((1==n)||((n=isprimepower(n))&&!(n%2)));

Crossrefs

Characteristic function of A056798.

Cf. A010055, A302048, A353817.

Sequence in context: A014999 A227291 A271102 * A353374 A326072 A304362

Adjacent sequences: A353797 A353798 A353799 * A353801 A353802 A353803

Keyword

nonn

Author

Antti Karttunen, May 15 2022

Status

approved