0,4

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 inA227107.Thus a(n) is related to denominator of the harmonic mean H(n-4, 4).

Note the difference fromA000265(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.

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

Andrew Howroyd,Table of n, a(n) for n = 0..1000

Peter Bala,A note on the sequence of numerators of a rational function,2019.

Index entries for linear recurrences with constant coefficients,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).

a(n) = n/gcd(n, 2^5).

a(n) = denominator(8*(n-4)/n), n >= 0 (with denominator(infinity) = 0).

FromPeter Bala,Feb 27 2019: (Start)

a(n) = numerator(n/(n + 32)).

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)

FromBernard Schott,Mar 02 2019: (Start)

a(n) = 1 iff n is 1, 2, 4, 8, 16, 32 and a(2^n) = 2^(n-5) for n >= 5.

a(n) = n iff n is odd (A005408). (End)

FromAmiram Eldar,Nov 25 2022: (Start)

Multiplicative with a(2^e) = 2^(e-min(e,5)), and a(p^e) = p^e for p > 2.

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)).

Sum_{k=1..n} a(k) ~ (683/2048) * n^2. (End)

seq(n/igcd(n, 32), n=0..70); #Muniru A Asiru,Feb 28 2019

With[{c=2^5}, Table[n/GCD[n, c], {n, 0, 70}]] (*Harvey P. Dale,Feb 16 2018 *)

(PARI) a(n)=n/gcd(n, 2^5); \\Andrew Howroyd,Jul 23 2018

(Magma) [n/GCD(n, 2^5): n in [0..80]]; //G. C. Greubel,Feb 27 2019

(Sage) [n/gcd(n, 2^5) for n in (0..80)] #G. C. Greubel,Feb 27 2019

(GAP) List([0..80], n-> n/Gcd(n, 2^5)); #G. C. Greubel,Feb 27 2019

Cf.A000265,A227042,A227107,A106617,A276234.

Sequence in context:A161955A276234A000265*A106617A040026A106609

Adjacent sequences:A227137A227138A227139*A227141A227142A227143

nonn,frac,easy,mult

Wolfdieter Lang,Jul 04 2013

Keyword:mult added byAndrew Howroyd,Jul 23 2018

approved