A355823 a(n) = 1 if all exponents in prime factorization of n are powers of 2, otherwise 0.

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

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

Multiplicative with a(p^e) = A209229(e).

For all n >= 1, A302777(n) <= a(n) <= A355825(n).

a(n) = A091862(A225546(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A271727. - Amiram Eldar, Jul 23 2022

Example

For n = 8 = 2^3, a(8) = 0 as 3 is not a power of 2 (in A000079).

Mathematica

a[n_] := If[AllTrue[FactorInteger[n][[;; , 2]], # == 2^IntegerExponent[#, 2] &], 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 19 2022 *)

Prog

(PARI) A355823(n) = factorback(apply(e->!bitand(e, e-1), factor(n)[, 2]));

Crossrefs

Characteristic function of A138302, "Exponentially 2^n-numbers".

Cf. A000079, A091862, A209229, A225546, A271727, A302777, A355824 (Dirichlet inverse).

Differs from related A355825 for the first time at n=128, where a(128) = 0, while A355825(128) = 1.

Sequence in context: A077010 A330548 A225817 * A355825 A332732 A248863

Adjacent sequences: A355820 A355821 A355822 * A355824 A355825 A355826

Keyword

nonn,mult

Author

Antti Karttunen, Jul 19 2022

Status

approved