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%I #10 Jun 17 2024 07:12:07
%S 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,
%T 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,
%U 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
%N a(n) = 1 if the exponent of 2 in their canonical prime factorization is equal to the maximal exponent, otherwise 0.
%H Antti Karttunen, <a href="/A373252/b373252.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = [A007814(n) == A051903(n)], where [ ] is the Iverson bracket.
%F 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
%t a[n_] := If[IntegerExponent[n, 2] == Max[FactorInteger[n][[;; , 2]]], 1, 0]; a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Jun 17 2024 *)
%o (PARI) A373252(n) = (1==n || (vecmax(factor(n)[, 2]) == valuation(n, 2))); \\ (after function "is" in A360015) - _Antti Karttunen_, Jun 13 2024
%Y Characteristic function of A360015.
%Y Cf. A007814, A309155.
%K nonn
%O 1
%A _Antti Karttunen_, Jun 13 2024
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