A072073 Number of solutions to cototient(x) = A051953(x) = 2^n.

1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10

Offset: 1

Author

Labos Elemer, Jun 13 2002

Keywords

• nonn

Comments

a(n) increases at A000043(n).

Since A051953(p) = 1 for p prime, and given that there are an infinite number of primes, we disregard a(0) = oo. - Michael De Vlieger, Mar 25 2020

Examples

			InvCototient(2^0) has an infinite number of entries, so 2^0=1 is left out.
n=14: 2^14=16384, InvCototient(16384) = {24576,28672,31744,32512,32764,32768}, so a(14)=6;
		

Crossrefs

Cf. A051953, A058764, A000043, A063740, A000079.

Programs

Mathematica

Length /@ Most@ Split@ DeleteCases[Select[Array[# - EulerPhi[#] &, 10^6], IntegerQ@ Log2@ # &], 1] (* Michael De Vlieger, Mar 25 2020 *)

Formula

a(n) = A063740(A000079(n)). - Ridouane Oudra, Jun 02 2024