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A274139 a(n) = 2^A000265(n) = 2^numerator(n/2^n), a sequence related to Oresme numbers.

%I A274139 #16 Jan 05 2025 19:51:40
%S A274139 2,2,8,2,32,8,128,2,512,32,2048,8,8192,128,32768,2,131072,512,524288,
%T A274139 32,2097152,2048,8388608,8,33554432,8192,134217728,128,536870912,
%U A274139 32768,2147483648,2,8589934592,131072,34359738368,512,137438953472,524288,549755813888,32
%N A274139 a(n) = 2^A000265(n) = 2^numerator(n/2^n), a sequence related to Oresme numbers.
%C A274139 Differences: 0, 6, -6, 30, -24, 120, -126, 510, -480, 2016, -2040, 8184, -8064, 32640, -32766, 131070, -130560, ...
%C A274139 GCD of differences is 6.
%H A274139 A. F. Horadam, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/12-3/horadam.pdf">Oresme numbers</a>, Fib. Quart., 12 (1974), 267-271.
%F A274139 a(n) = 2^denominator(2^n/n).
%F A274139 a(n) = 2^(n/2^valuation(n,2)) = 2^A007814(n).
%F A274139 a(n) = 2*A082392(n)^2 (conjecture).
%t A274139 a[n_] := 2^(n/2^IntegerExponent[n, 2]);
%t A274139 Array[a, 40]
%o A274139 (PARI) a(n) = 2^(n/2^valuation(n,2)); \\ _Michel Marcus_, Jun 12 2016
%Y A274139 Cf. A000265, A006519, A007814, A082392.
%K A274139 nonn
%O A274139 1,1
%A A274139 _Jean-François Alcover_ and _Paul Curtz_, Jun 11 2016