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

0,2

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

Links

Table of n, a(n) for n=0..50.

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

Example

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};
...

Prog

(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

Crossrefs

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

Sequence in context: A131753 A330319 A171503 * A283008 A283259 A284090

Adjacent sequences: A326351 A326352 A326353 * A326355 A326356 A326357

Keyword

nonn

Author

Stefano Spezia, Jul 06 2019

Status

approved