A319710 a(n) = 1 if n is divisible by the square of its smallest prime factor, 0 otherwise.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Formula

a(n) = 1 iff A067029(n) > 1.

a(n) = 1 if A020639(n)^2 divides n, otherwise 0.

a(n) = 1 iff n > 1 and A126773(n) = 1.

a(4*n) = a(18*n + 9) = 1. - David A. Corneth, Oct 04 2018

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A283071. - Amiram Eldar, Jul 24 2022

Mathematica

Join[{0}, Table[If[Divisible[n, FactorInteger[n][[1, 1]]^2], 1, 0], {n, 2, 130}]] (* Harvey P. Dale, Mar 01 2019 *)

Prog

(PARI) A319710(n) = ((n>1)&&(factor(n)[1, 2]>1));

Crossrefs

Characteristic function of A283050.

Cf. A008966, A020639, A067029, A010052, A126773, A268340, A283071, A319988.

Sequence in context: A319988 A023969 A060039 * A345951 A345952 A359466

Adjacent sequences: A319707 A319708 A319709 * A319711 A319712 A319713

Keyword

nonn

Author

Antti Karttunen, Oct 04 2018

Status

approved