This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227140 #49 Apr 19 2023 19:11:14
%S A227140 0,1,1,3,1,5,3,7,1,9,5,11,3,13,7,15,1,17,9,19,5,21,11,23,3,25,13,27,7,
%T A227140 29,15,31,1,33,17,35,9,37,19,39,5,41,21,43,11,45,23,47,3,49,25,51,13,
%U A227140 53,27,55,7,57,29,59,15,61,31,63,2,65,33,67,17,69,35
%N A227140 a(n) = n/gcd(n,2^5), n >= 0.
%C A227140 H(n,4) = 2*n*4/(n+4) is the harmonic mean of n and 4. For n >= 4 the denominator of H(n,4) is (n+4)/gcd(8*n,n+4) = (n+4)/gcd(n+4,32). a(n+8) = A227042(n+4,4), n >= 0. The numerator of H(n,4) is given in A227107. Thus a(n) is related to denominator of the harmonic mean H(n-4, 4).
%C A227140 Note the difference from A000265(n) (odd part of n) = n/gcd(n,2^n), n >= 1, which differs for the first time for n = 64. a(64) = 2, not 1.
%C A227140 A multiplicative sequence. Also, a(n) is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for n >= 1, m >= 1. In particular, a(n) is a divisibility sequence: if n divides m then a(n) divides a(m). - _Peter Bala_, Feb 27 2019
%H A227140 Andrew Howroyd, <a href="/A227140/b227140.txt">Table of n, a(n) for n = 0..1000</a>
%H A227140 Peter Bala, <a href="/A306367/a306367.pdf">A note on the sequence of numerators of a rational function</a>, 2019.
%H A227140 <a href="/index/Rec#order_64">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F A227140 a(n) = n/gcd(n, 2^5).
%F A227140 a(n) = denominator(8*(n-4)/n), n >= 0 (with denominator(infinity) = 0).
%F A227140 From _Peter Bala_, Feb 27 2019: (Start)
%F A227140 a(n) = numerator(n/(n + 32)).
%F A227140 O.g.f.: F(x) - F(x^2) - F(x^4) - F(x^8) - F(x^16) - F(x^32), where F(x) = x/(1 - x)^2. Cf. A106617. (End)
%F A227140 From _Bernard Schott_, Mar 02 2019: (Start)
%F A227140 a(n) = 1 iff n is 1, 2, 4, 8, 16, 32 and a(2^n) = 2^(n-5) for n >= 5.
%F A227140 a(n) = n iff n is odd (A005408). (End)
%F A227140 From _Amiram Eldar_, Nov 25 2022: (Start)
%F A227140 Multiplicative with a(2^e) = 2^(e-min(e,5)), and a(p^e) = p^e for p > 2.
%F A227140 Dirichlet g.f.: zeta(s-1)*(1 - 1/2^s - 1/2^(2*s) - 1/2^(3*s) - 1/2^(4*s) - 1/2^(5*s)).
%F A227140 Sum_{k=1..n} a(k) ~ (683/2048) * n^2. (End)
%p A227140 seq(n/igcd(n,32),n=0..70); # _Muniru A Asiru_, Feb 28 2019
%t A227140 With[{c=2^5},Table[n/GCD[n,c],{n,0,70}]] (* _Harvey P. Dale_, Feb 16 2018 *)
%o A227140 (PARI) a(n)=n/gcd(n, 2^5); \\ _Andrew Howroyd_, Jul 23 2018
%o A227140 (Magma) [n/GCD(n, 2^5): n in [0..80]]; // _G. C. Greubel_, Feb 27 2019
%o A227140 (Sage) [n/gcd(n,2^5) for n in (0..80)] # _G. C. Greubel_, Feb 27 2019
%o A227140 (GAP) List([0..80], n-> n/Gcd(n, 2^5)); # _G. C. Greubel_, Feb 27 2019
%Y A227140 Cf. A000265, A227042, A227107, A106617, A276234.
%K A227140 nonn,frac,easy,mult
%O A227140 0,4
%A A227140 _Wolfdieter Lang_, Jul 04 2013
%E A227140 Keyword:mult added by _Andrew Howroyd_, Jul 23 2018