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

1,3

Comments

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

Links

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

Example

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]

Mathematica

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

Prog

(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

Crossrefs

Cf. A051953, A053577, A058764, A007283.

Sequence in context: A126210 A040005 A193306 * A368201 A168177 A216864

Adjacent sequences: A053575 A053576 A053577 * A053579 A053580 A053581

Keyword

nonn

Author

Labos Elemer, Jan 18 2000

Extensions

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

Status

approved