A072455 Number of totients in the reduced residue system of 2n-1.
1, 2, 3, 4, 4, 6, 7, 4, 8, 9, 7, 11, 10, 8, 13, 14, 9, 11, 16, 10, 17, 18, 9, 20, 19, 13, 22, 17, 15, 25, 26, 14, 21, 28, 16, 29, 30, 14, 23, 31, 19, 33, 27, 19, 35, 28, 22, 29, 37, 19, 38, 39, 16, 41, 42, 26, 44, 33, 26, 38, 41, 27, 36, 47, 29, 49, 43, 22, 51, 52, 32, 43, 40, 27
Offset: 1
Keywords
Examples
For n=31: reduced residue system(31) = {1,...,30} with 15 odd and 15 even numbers. From the odd terms only the term 1 is totient, while from the 15 even terms, 2 terms, {14,26}, are nontotients, so 13 terms are totients. All totients count 1 + 13 = 14, thus a((31+1)/2) = a(16) = 14.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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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) = phi(2*n-1) - A072454(n). [Corrected by Sean A. Irvine, Oct 04 2024]