A373252 a(n) = 1 if the exponent of 2 in their canonical prime factorization is equal to the maximal exponent, otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

a(n) = [A007814(n) == A051903(n)], where [ ] is the Iverson bracket.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=2} 1/(zeta(k)*(2^k-1)) = 0.44541445377638761933... . - Amiram Eldar, Jun 17 2024

Mathematica

a[n_] := If[IntegerExponent[n, 2] == Max[FactorInteger[n][[;; , 2]]], 1, 0]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Jun 17 2024 *)

Prog

(PARI) A373252(n) = (1==n || (vecmax(factor(n)[, 2]) == valuation(n, 2))); \\ (after function "is" in A360015) - Antti Karttunen, Jun 13 2024

Crossrefs

Characteristic function of A360015.

Cf. A007814, A309155.

Sequence in context: A178225 A373990 A264739 * A257170 A073097 A117569

Adjacent sequences: A373249 A373250 A373251 * A373253 A373254 A373255

Keyword

nonn

Author

Antti Karttunen, Jun 13 2024

Status

approved