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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 26 17:40 EDT 2020. Contains 334630 sequences. (Running on oeis4.)