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A373252
a(n) = 1 if the exponent of 2 in their canonical prime factorization is equal to the maximal exponent, otherwise 0.
1
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
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.
Sequence in context: A178225 A373990 A264739 * A257170 A073097 A117569
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 13 2024
STATUS
approved