A359429 a(n) = 1 if n is cubefree, but not squarefree, 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, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1

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) = A107078(n) * A212793(n) = A212793(n) - A008966(n).

a(n) = [A072411(n) == 2] = [A290107(n) == 2], where [ ] is the Iverson bracket.

a(n) >= A359474(n).

Sum_{k=1..n} a(k) ~ c * n, where c = 1/zeta(3) - 1/zeta(2) = A088453 - A059956 = 0.22398... . - Amiram Eldar, Jan 05 2023

Mathematica

a[n_] := If[Max[FactorInteger[n][[;; , 2]]] == 2, 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 05 2023 *)

Prog

(PARI)
A212793(n) = {f = factor(n); for (i=1, #f~, if ((f[i, 2]) >=3, return(0)); ); return (1); }; \\ From A212793.
A359429(n) = (A212793(n)-issquarefree(n));

Crossrefs

Characteristic function of A067259.

Cf. A008966, A072411, A107078, A212793, A290107, A359474.

Cf. A059956, A088453.

Sequence in context: A284954 A221151 A359474 * A353470 A342753 A358752

Adjacent sequences: A359426 A359427 A359428 * A359430 A359431 A359432

Keyword

nonn

Author

Antti Karttunen, Jan 04 2023

Status

approved