|
%I #14 Jun 09 2024 09:05:25
%S 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,
%T 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,
%U 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
%N Values of cototient function for A053577.
%C Except for 2^0 = 1, there are only finitely many values of k such that cototient(k) = 2^m for fixed m.
%H Amiram Eldar, <a href="/A053578/b053578.txt">Table of n, a(n) for n = 1..10000</a>
%e 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]
%t Select[Table[k - EulerPhi[k], {k, 1, 400}], # == 2^IntegerExponent[#, 2] &] (* _Amiram Eldar_, Jun 09 2024 *)
%o (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
%Y Cf. A051953, A053577, A058764, A007283.
%K nonn
%O 1,3
%A _Labos Elemer_, Jan 18 2000
%E Edited and corrected by _M. F. Hasler_, Nov 10 2016
|
