A396553 - OEIS

%I #8 May 29 2026 06:14:21

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,24,25,26,28,30,

%T 31,32,33,34,35,36,39,40,41,42,44,45,48,50,51,52,55,56,60,61,62,63,64,

%U 65,66,68,70,72,75,77,78,80,82,84,85,88,90,91,93,96,97,99,100,102,103

%N Numbers k such that EulerPhi(psi(k)) is a power of 2, where psi = A002322 is the reduced totient function.

%C Numbers k such that psi(k) is in A003401.

%C Numbers k such that values taken by chi are all constructible numbers for all Dirichlet characters chi modulo k.

%H Jianing Song, <a href="/A396553/b396553.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Constructible_number">Constructible number</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dirichlet_character">Dirichlet character</a>.

%e The Dirichlet characters modulo 103 have orders 1, 2, 3, 6, 17, 34, 51, or 102. Since exp(2*Pi*I/d) is always a constructible number when d takes these values (in other words, a regular polygon with 3, 6, 17, 34, 51, or 102 sides can be constructed with compass and straightedge), 103 is a term.

%o (PARI) ispower2(n) = (bitand(n,n-1) == 0)

%o isA396553(n) = ispower2(eulerphi(A002322(n))) \\ see A002322 for its program

%Y Cf. A002322, A003401, A335120 (prime terms), A396554 (complement).

%K nonn

%O 1,2

%A _Jianing Song_, May 29 2026