A359474 a(n) = 1 if the product of exponents in the prime factorization of n is 2, otherwise 0.

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

Offset

1

Comments

a(n) = 1 if there is exactly one exponent in the prime factorization of n that is larger than 1, and that exponent is 2, otherwise 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions.

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

Formula

a(n) = [A005361(n) == 2], where [ ] is the Iverson bracket.

a(n) = [A000688(n) == 2].

a(n) = [A046660(n) == 1].

a(n) = A359471(n) - A008966(n).

a(n) = A302048(n) + A359475(n).

a(n) = A359429(n) * A359466(n).

Sum_{k=1..n} a(k) ~ c * n, where c = A271971. - Amiram Eldar, Jan 05 2023

Mathematica

a[n_] := If[PrimeOmega[n] - PrimeNu[n] == 1, 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 05 2023 *)

Prog

(PARI) A359474(n) = (2==factorback(factor(n)[, 2])); \\ From the "is" function given in A048109

Crossrefs

Characteristic function of A060687.

Cf. A000688, A005361, A008966, A046660, A271971, A302048, A359429, A359466, A359471, A359472, A359475.

Sequence in context: A295308 A284954 A221151 * A359429 A353470 A342753

Adjacent sequences: A359471 A359472 A359473 * A359475 A359476 A359477

Keyword

nonn

Author

Antti Karttunen, Jan 04 2023

Status

approved