A359466 a(n) = 1 if n has exactly one non-unitary prime factor, otherwise 0.

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 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) = [A056170(n) == 1], where [ ] is the Iverson bracket.

a(n) = A353670(A181819(n)).

a(n) >= A359472(n) and a(n) >= A359474(n).

Sum_{k=1..n} a(k) ~ c * n, where c = A059956 * A154945 = 0.335389... . - Amiram Eldar, Jan 05 2023

Mathematica

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

Prog

(PARI) A359466(n) = { my(f=factor(n)); (1==#select(x->(x>1), f[, 2])); }; \\ After isok function in A190641

Crossrefs

Characteristic function of A190641.

Cf. A056170, A181819, A353670, A359472, A359474.

Differs from A359467 for the first time at n=225, where a(225) = 0, while A359467(225) = 1.

Cf. A059956, A154945.

Sequence in context: A319710 A345951 A345952 * A359467 A359469 A107078

Adjacent sequences: A359463 A359464 A359465 * A359467 A359468 A359469

Keyword

nonn

Author

Antti Karttunen, Jan 02 2023

Status

approved