A359471 a(n) = 1 if the product of exponents in the prime factorization of n is less than 3, otherwise 0.

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

Offset

1

Comments

a(n) = 1 if there are more unitary divisors of n (A034444) than non-unitary divisors of n (A048105), 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) < 3], where [ ] is the Iverson bracket.

a(n) = [A046660(n) < 2].

a(n) = [A048106(n) > 0].

a(n) = [A359431(n) == 0] = [A325973(n) == A326043(n)].

a(n) = A008966(n) + A359474(n).

a(n) >= A359475(n).

Sum_{k=1..n} a(k) ~ c * n, where c = A059956 + A271971 = 0.8086828238... . - Amiram Eldar, Jan 05 2023

Mathematica

a[n_] := If[2^(1 + PrimeNu[n]) > DivisorSigma[0, n], 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 05 2023 *)

Prog

(PARI) A359471(n) = { (1==n) || (factorback(factor(n)[, 2])<3); }; \\ After function "is" given in A048107.

Crossrefs

Characteristic function of A048107.

Cf. A005361, A008966, A034444, A048105, A048106, A325973, A326043, A359431, A359472, A359474, A359475.

Cf. A059956, A271971.

Sequence in context: A305940 A119981 A115789 * A363551 A053864 A189021

Adjacent sequences: A359468 A359469 A359470 * A359472 A359473 A359474

Keyword

nonn

Author

Antti Karttunen, Jan 04 2023

Status

approved