A062823 Numbers k such that the number of divisors of k divides the number of divisors of the totient of k.
1, 3, 7, 11, 13, 14, 15, 19, 22, 23, 25, 28, 29, 31, 35, 39, 41, 43, 44, 46, 47, 50, 53, 55, 56, 59, 61, 62, 67, 68, 70, 71, 73, 77, 78, 79, 82, 83, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 103, 107, 109, 110, 111, 112, 113, 115, 117, 118, 119, 122, 124, 127, 129, 131
Offset: 1
Keywords
Examples
For k = {3,11,29}, phi(k) = {2,10,28}, d(phi(k)) = {2,4,6}, d(k) = 2, quotient = {1,2,3}.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1001 from Harry J. Smith)
Programs
-
Mathematica
Select[Range@ 132, Mod @@ DivisorSigma[0, {EulerPhi@ #, #}] == 0 &] (* Michael De Vlieger, Jun 29 2018 *) -
PARI
select(m->frac(numdiv(eulerphi(m))/numdiv(m)) == 0, [1..500]) \\ Harry J. Smith, Aug 11 2009
-
PARI
isok(k) = {my(f = factor(k)); !(numdiv(eulerphi(f)) % numdiv(f));} \\ Amiram Eldar, Jan 31 2025
Extensions
Incorrect formula deleted by Jon E. Schoenfield, Jul 02 2018
Offset corrected by Amiram Eldar, Jan 31 2025