A276234 a(n) = n/gcd(n, 256).
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, 29, 15, 31, 1, 33, 17, 35, 9, 37, 19, 39, 5, 41, 21, 43, 11, 45, 23, 47, 3, 49, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 15, 61, 31, 63, 1, 65, 33, 67, 17, 69, 35, 71
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
- Peter Bala, A note on the sequence of numerators of a rational function, 2019.
- Index entries for linear recurrences with constant coefficients, order 512.
Programs
-
GAP
List([1..80], n-> n/Gcd(n, 2^8)); # G. C. Greubel, Feb 27 2019
-
Magma
[n/GCD(n, 2^8): n in [1..80]]; // G. C. Greubel, Feb 27 2019
-
Maple
seq(n/igcd(n,256), n=1..100); # Robert Israel, Aug 26 2016
-
Mathematica
Table[n/GCD[n, 2^8], {n,1,80}] (* G. C. Greubel, Feb 27 2019 *) -
PARI
a(n)=n/gcd(n,256) \\ Charles R Greathouse IV, Aug 26 2016
-
Sage
[n/gcd(n, 2^8) for n in (1..80)] # G. C. Greubel, Feb 27 2019
Formula
a(2k-1) = 2k-1.
G.f.: (x+x^3)/(1-x^2)^2 +(x^2+x^6)/(1-x^4)^2 +(x^4+x^12)/(1-x^8)^2 +(x^8+x^24)/(1-x^16)^2 +(x^16+x^48)/(1-x^32)^2 +(x^32+x^96)/(1-x^64)^2 +(x^64+x^192)/(1-x^128)^2 +(x^128+x^256+x^384)/(1-x^256)^2. - Robert Israel, Aug 26 2016
a(n) = 2*a(n-256) - a(n-512). - Charles R Greathouse IV, Aug 26 2016
From Peter Bala, Feb 27 2019: (Start)
a(n) = numerator(n/(n + 256)).
O.g.f.: F(x) - Sum_{k = 1..8} F(x^(2^k)), where F(x) = x/(1 - x)^2. Cf. A106617. (End)
From Amiram Eldar, Nov 26 2022: (Start)
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) - 1/2^(6*s) - 1/2^(7*s) - 1/2^(8*s)).
Multiplicative with a(2^e) = 2^(e-min(e,8)), and a(p^e) = p^e for p > 2.
Sum_{k=1..n} a(k) ~ (43691/131072) * n^2. (End)
Extensions
Keyword:mult added and terms a(51) and beyond from Andrew Howroyd, Jul 23 2018
Comments