A359475 a(n) = 1 if n is a cubefree nonsquare whose factorization into a product of primes contains exactly one square, otherwise 0.

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

Offset

1

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) = A049240(n) * A359474(n) = A359474(n) - A302048(n).

a(n) <= A359471(n).

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

Mathematica

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

Prog

(PARI) A359475(n) = (omega(n) > 1) && (bigomega(n) - omega(n) == 1); \\ From "isok" function given in A072357 by Michel Marcus, Jul 16 2015

Crossrefs

Characteristic function of A072357.

Cf. A049240, A271971, A302048, A359471, A359474.

Sequence in context: A323547 A294930 A353472 * A294937 A363131 A355447

Adjacent sequences: A359472 A359473 A359474 * A359476 A359477 A359478

Keyword

nonn

Author

Antti Karttunen, Jan 04 2023

Status

approved