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A075101
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Numerator of 2^n/n.
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15
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2, 2, 8, 4, 32, 32, 128, 32, 512, 512, 2048, 1024, 8192, 8192, 32768, 4096, 131072, 131072, 524288, 262144, 2097152, 2097152, 8388608, 2097152, 33554432, 33554432, 134217728, 67108864, 536870912, 536870912, 2147483648, 134217728, 8589934592, 8589934592, 34359738368, 17179869184, 137438953472
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 2^n/gcd(n,2^n).
O.g.f.: F(2*x) - (1/2)*F((2*x)^2) - (1/4)*F((2*x)^4) - (1/8)*F((2*x)^8) - ..., where F(x) = x/(1 - x). Cf. A000265.
O.g.f. for reciprocals: Sum_{n >= 1} x^n/a(n) = F((x/2)) + F((x/2)^2) + 2*F((x/2)^4) + 4*F((x/2)^8) + 8*F((x/2)^16) + 16*F((x/2)^32) + .... (End)
Sum_{n>=1} 1/a(n) = Sum_{n>=1} 2^(2^(n-1)+n-1)/(2^(2^n) - 1) = Sum_{n>=1} A073113(n-1)/A051179(n) = 1.48247501707... - Amiram Eldar, Aug 14 2022
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MAPLE
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[seq(numer(2^n/n), n=1..50)];
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MATHEMATICA
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PROG
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(Python)
from fractions import Fraction
return (Fraction(2**n)/n).numerator # Chai Wah Wu, Mar 25 2018
(PARI) a(n) = 2^(n - valuation(n, 2)) \\ Jianing Song, Oct 24 2018
(Magma) [Numerator(2^n/n): n in [1..50]]; // G. C. Greubel, Feb 28 2019
(Sage) [numerator(2^n/n) for n in (1..50)] # G. C. Greubel, Feb 28 2019
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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