A326354 a(n) is the number of fractions reduced to lowest terms with numerator and denominator less than or equal to n in absolute value.

1, 3, 7, 15, 23, 39, 47, 71, 87, 111, 127, 167, 183, 231, 255, 287, 319, 383, 407, 479, 511, 559, 599, 687, 719, 799, 847, 919, 967, 1079, 1111, 1231, 1295, 1375, 1439, 1535, 1583, 1727, 1799, 1895, 1959, 2119, 2167, 2335, 2415, 2511, 2599, 2783, 2847, 3015, 3095

Offset: 0

Author

Stefano Spezia, Jul 06 2019

Keywords

• nonn

Comments

All the terms of this sequence are odd numbers (A005408).

For n > 1, a(n) is congruent to 7 mod 8 (A004771).

Apart from a(0) the same as A171503. - R. J. Mathar, Sep 03 2019

Examples

			a(0) = 1 since X(0) = {0};
a(1) = 3 since X(1) = {-1, 0, 1};
a(2) = 7 since X(2) = {-2, -1, -1/2, 0, 1/2, 1, 2};
a(3) = 15 since X(3) = {-3, -2, -3/2, -1, -2/3, -1/2, -1/3, 0, 1/3, 1/2, 2/3, 1, 3/2, 2, 3};
...
		

Crossrefs

Cf. A000010, A004771, A005408, A171503, A206350.

Programs

Magma

I:=[1, 3]; [n le 2 select I[n] else Self(n-1)+4*EulerPhi(n-1): n in [1..51]];

PARI

nmax = 50; a=vector(nmax+1); a[1]=1; a[2]=3; for(n=3, nmax+1, a[n]=a[n-1]+4*eulerphi(n-1)); a

Formula

a(0) = 1, a(1) = 3 and a(n) = a(n-1) + 4*A000010(n) for n > 1, where A000010(n) = phi(n).

a(n) = 2*A206350(n+1) - 1. - Michel Marcus, Jul 07 2019