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

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, 30, 23, 21, 33, 34, 22, 27, 38, 28, 41, 42, 26, 37, 47, 35, 49, 37, 37, 53, 44, 38, 43, 59, 41, 62, 63, 32, 65, 66, 46, 68, 55, 46, 58, 69, 53, 64, 79, 55, 81, 65, 50, 85, 86, 60, 77, 72

Offset: 1

Author

Labos Elemer, Jun 19 2002

Keywords

• nonn

Examples

			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.
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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A002202, A005277, A037225, A072451, A072455.

Bisection of A072106.

Programs

PARI

a(n) = {my(m = 2*n-1); sum(k = 1, m, gcd(m, k) == 1 && !istotient(k));} \\ Amiram Eldar, Nov 07 2024

Formula

a(n) = A072106(2*n-1). - Amiram Eldar, Nov 07 2024