cp's OEIS Frontend

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.

%I A326354 #35 Sep 08 2022 08:46:24
%S A326354 1,3,7,15,23,39,47,71,87,111,127,167,183,231,255,287,319,383,407,479,
%T A326354 511,559,599,687,719,799,847,919,967,1079,1111,1231,1295,1375,1439,
%U A326354 1535,1583,1727,1799,1895,1959,2119,2167,2335,2415,2511,2599,2783,2847,3015,3095
%N 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.
%C A326354 All the terms of this sequence are odd numbers (A005408).
%C A326354 For n > 1, a(n) is congruent to 7 mod 8 (A004771).
%C A326354 Apart from a(0) the same as A171503. - _R. J. Mathar_, Sep 03 2019
%F A326354 a(0) = 1, a(1) = 3 and a(n) = a(n-1) + 4*A000010(n) for n > 1, where A000010(n) = phi(n).
%F A326354 a(n) = 2*A206350(n+1) - 1. - _Michel Marcus_, Jul 07 2019
%e A326354 a(0) = 1 since X(0) = {0};
%e A326354 a(1) = 3 since X(1) = {-1, 0, 1};
%e A326354 a(2) = 7 since X(2) = {-2, -1, -1/2, 0, 1/2, 1, 2};
%e A326354 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};
%e A326354 ...
%o A326354 (Magma) I:=[1, 3]; [n le 2 select I[n] else Self(n-1)+4*EulerPhi(n-1): n in [1..51]];
%o A326354 (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
%Y A326354 Cf. A000010, A004771, A005408, A171503, A206350.
%K A326354 nonn
%O A326354 0,2
%A A326354 _Stefano Spezia_, Jul 06 2019