A008831 -id:A008831 - cp's OEIS frontend

A002246 a(1) = 3; for n > 1, a(n) = 4*phi(n); given a rational number r = p/q, where q>0, (p,q)=1, define its height to be max{|p|,q}; then a(n) = number of rational numbers of height n.

3, 4, 8, 8, 16, 8, 24, 16, 24, 16, 40, 16, 48, 24, 32, 32, 64, 24, 72, 32, 48, 40, 88, 32, 80, 48, 72, 48, 112, 32, 120, 64, 80, 64, 96, 48, 144, 72, 96, 64, 160, 48, 168, 80, 96, 88, 184, 64, 168, 80, 128, 96, 208, 72, 160, 96, 144, 112, 232, 64, 240, 120, 144, 128, 192, 80, 264

Offset: 1

N. J. A. Sloane, Nov 02 2008

nonn

The old entry with this sequence number was a duplicate of A008831.

a(n) is also the number of integers prime to n in the interval [n+1, 5n-1]. [From Washington Bomfim, Oct 10 2009]

			The three rational numbers of height 1 are 0, 1 and -1.

M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 7.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000010, A097080.

A002246(n) = if(1==n,3,4*eulerphi(n)); \\ Antti Karttunen, Dec 05 2017

a(1) = 3; thereafter a(n) = 4*phi(n) = 4*A000010(n).

A simpler alternative description added to the name field by Antti Karttunen, Dec 05 2017

A036118 a(n) = 2^n mod 13.

Original entry on oeis.org

1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7

Offset: 0

N. J. A. Sloane

The sequence is 12-periodic.

I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,-1,1).

Cf. A008831.

List([0..95],n->PowerMod(2,n,13)); # Muniru A Asiru, Jan 31 2019

[2^n mod 13: n in [0..100]]; // G. C. Greubel, Oct 16 2018

[ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];

PowerMod[2, Range[0, 70], 13] (* Wesley Ivan Hurt, Nov 20 2014 *)

a(n)=2^n%13 \\ Charles R Greathouse IV, Oct 07 2015

[power_mod(2,n,13) for n in range(0,72)] # Zerinvary Lajos, Nov 03 2009

a(n) = 13/2 + (-5/3 - (2/3)*sqrt(3))*cos(Pi*n/6) + (-1/3 - sqrt(3))*sin(Pi*n/6) - (13/6)*cos(Pi*n/2) - (13/6)*sin(Pi*n/2) + (-5/3 + (2/3)*sqrt(3))*cos(5*Pi*n/6) + (sqrt(3) - 1/3)*sin(5*Pi*n/6). - Richard Choulet, Dec 12 2008
a(n) = a(n-1) - a(n-6) + a(n-7). - R. J. Mathar, Apr 13 2010
G.f.: (1 + x + 2*x^2 + 4*x^3 - 5*x^4 + 3*x^5 + 7*x^6)/ ((1-x) * (x^2+1) * (x^4 - x^2 + 1)). - R. J. Mathar, Apr 13 2010
a(n) = 13 - a(n+6) = a(n+12) for all n in Z. - Michael Somos, Oct 17 2018

cp's OEIS Frontend

A002246 a(1) = 3; for n > 1, a(n) = 4*phi(n); given a rational number r = p/q, where q>0, (p,q)=1, define its height to be max{|p|,q}; then a(n) = number of rational numbers of height n.

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