A053578 Values of cototient function for A053577.

1, 1, 2, 1, 4, 1, 4, 1, 8, 1, 8, 8, 1, 1, 1, 16, 16, 1, 1, 16, 1, 1, 1, 1, 32, 1, 32, 1, 1, 32, 32, 1, 1, 1, 1, 1, 1, 64, 1, 1, 1, 1, 1, 64, 1, 64, 1, 64, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 128, 1, 1, 1, 1, 1, 128, 1, 1, 1, 1, 1, 128, 1, 128, 128, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Labos Elemer, Jan 18 2000

Keywords

• nonn

Comments

Except for 2^0 = 1, there are only finitely many values of k such that cototient(k) = 2^m for fixed m.

Examples

			For p prime, cototient(p) = 1. Smallest values for which cototient(x) = 2^w are A058764(w) = A007283(w-1) = 3*2^(w-1) = 6, 12, 24, 48, 96, 192, .., 49152 for w = 2, 3, 4, 5, 6, ..., 15. [Corrected by _M. F. Hasler_, Nov 10 2016]
		

Links

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

Crossrefs

Cf. A051953, A053577, A058764, A007283.

Programs

Mathematica

Select[Table[k - EulerPhi[k], {k, 1, 400}], # == 2^IntegerExponent[#, 2] &] (* Amiram Eldar, Jun 09 2024 *)

PARI

lista(kmax) = {my(c); for(k = 2, kmax, c = k - eulerphi(k); if(c >> valuation(c, 2) == 1, print1(c, ", ")));} \\ Amiram Eldar, Jun 09 2024

Extensions

Edited and corrected by M. F. Hasler, Nov 10 2016