A380454 a(n) = 1 if the product of exponents in its prime factorization is greater than 3, otherwise 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, 1, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1

Comments

a(n) = 1 if n has less unitary divisors (A034444) than non-unitary divisors (A048105), otherwise 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100001

Index entries for characteristic functions.

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

Formula

a(n) = [A005361(n) > 3].

a(n) = [A046951(n) > 2].

a(n) = [A000005(n) > 2*A034444(n)] = [A000005(n) > 2^(1+A001221(n))], where [ ] is the Iverson bracket.

a(n) = [A034444(n) < A048105(n)] = [A048106(n) < 0].

a(n) = 1 - (A359471(n)+A359472(n)).

Sum_{k=1..n} a(k) ~ c*n, where c = A059956 * (1 + A085548) = 0.1171394347594477824... . - Amiram Eldar, Jan 29 2025

Mathematica

A380454[n_] := Boole[Times @@ FactorInteger[n][[All, 2]] > 3];
Array[A380454, 100] (* Paolo Xausa, Jan 28 2025 *)

Prog

(PARI) A380454(n) = (numdiv(n) > 2^(1+omega(n)));
(PARI) A380454(n) = (factorback(factor(n)[, 2])>3);

Crossrefs

Characteristic function of A048111.

Cf. A000005, A001221, A005361, A034444, A046951, A048105, A048106, A359471, A359472.

Cf. A059956, A085548.

Sequence in context: A358261 A380397 A295884 * A101637 A337380 A381036

Adjacent sequences: A380451 A380452 A380453 * A380455 A380456 A380457

Keyword

nonn

Author

Antti Karttunen, Jan 27 2025

Status

approved