

A276234


a(n) = n/gcd(n, 256).


3



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
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OFFSET

1,3


COMMENTS

a(n) first differs from A000265(n) at n = 512.  Andrew Howroyd, Jul 23 2018
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


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.


FORMULA

a(2k1) = 2k1.
G.f.: (x+x^3)/(1x^2)^2 +(x^2+x^6)/(1x^4)^2 +(x^4+x^12)/(1x^8)^2 +(x^8+x^24)/(1x^16)^2 +(x^16+x^48)/(1x^32)^2 +(x^32+x^96)/(1x^64)^2 +(x^64+x^192)/(1x^128)^2 +(x^128+x^256+x^384)/(1x^256)^2.  Robert Israel, Aug 26 2016
a(n) = 2*a(n256)  a(n512).  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(s1)*(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^(emin(e,8)), and a(p^e) = p^e for p > 2.
Sum_{k=1..n} a(k) ~ (43691/131072) * n^2. (End)


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 *)


PROG

(PARI) a(n)=n/gcd(n, 256) \\ Charles R Greathouse IV, Aug 26 2016
(Magma) [n/GCD(n, 2^8): n in [1..80]]; // G. C. Greubel, Feb 27 2019
(Sage) [n/gcd(n, 2^8) for n in (1..80)] # G. C. Greubel, Feb 27 2019
(GAP) List([1..80], n> n/Gcd(n, 2^8)); # G. C. Greubel, Feb 27 2019


CROSSREFS

Cf. A276233 (numerators), A227140, A000265, A106617.
Sequence in context: A327539 A072963 A161955 * A000265 A227140 A106617
Adjacent sequences: A276231 A276232 A276233 * A276235 A276236 A276237


KEYWORD

nonn,easy,mult,changed


AUTHOR

Artur Jasinski, Aug 24 2016


EXTENSIONS

Keyword:mult added and terms a(51) and beyond from Andrew Howroyd, Jul 23 2018


STATUS

approved



