cp's OEIS Frontend

A072454 Number of nontotients in the reduced residue system of 2n-1.

%I A072454 #19 Nov 07 2024 08:33:19
%S A072454 0,0,1,2,2,4,5,4,8,9,5,11,10,10,15,16,11,13,20,14,23,24,15,26,23,19,
%T A072454 30,23,21,33,34,22,27,38,28,41,42,26,37,47,35,49,37,37,53,44,38,43,59,
%U A072454 41,62,63,32,65,66,46,68,55,46,58,69,53,64,79,55,81,65,50,85,86,60,77,72
%N A072454 Number of nontotients in the reduced residue system of 2n-1.
%H A072454 Amiram Eldar, <a href="/A072454/b072454.txt">Table of n, a(n) for n = 1..10000</a>
%F A072454 a(n) = A072106(2*n-1). - _Amiram Eldar_, Nov 07 2024
%e A072454 For n=105: phi(105) = 48 with 24 odd, 24 even terms in the reduced residue system, of which 9 even terms and (all but 1) odd term is nontotient: a((105+1)/2) = a(53) = 24-1+9 = 32.
%e A072454 For n=21: reduced residue system(21) = Union({1,5,11,13,17,19}, {2,4,8,16,20}) includes 6 odd and 5 even numbers. No even nontotients terms in the reduced residue system(21), so 6-1 = 5 odd terms give all nontotients, so a((21+1)/2) = a(11) = 5.
%o A072454 (PARI) a(n) = {my(m = 2*n-1); sum(k = 1, m, gcd(m, k) == 1 && !istotient(k));} \\ _Amiram Eldar_, Nov 07 2024
%Y A072454 Cf. A000010, A002202, A005277, A037225, A072451, A072455.
%Y A072454 Bisection of A072106.
%K A072454 nonn
%O A072454 1,4
%A A072454 _Labos Elemer_, Jun 19 2002