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%I #12 Sep 12 2019 15:03:02
%S 27,43,109,125,157,229,277,283,307,499,643,691,733,739,811,997,1021,
%T 1051,1069,1093,1331,1459,1579,1597,1627,1699,1723,1789,1933,2179,
%U 2197,2203,2251,2341,2347,2749,2917,3163,3181,3229,3259,3373,4027,4339,4549,4597,4651,4909
%N Odd numbers k for which A006694((k-1)/2) = 3.
%C Conjecture. The terms of the sequence have only one prime divisor; moreover, p^3 is in the sequence if and only if p is in A001122.
%H Amiram Eldar, <a href="/A141229/b141229.txt">Table of n, a(n) for n = 1..10000</a>
%t r[n_] := EulerPhi[n]/MultiplicativeOrder[2, n]; Select[Range[5000], Total@(r /@ Divisors[#]) - 1 == 3 &] (* _Amiram Eldar_, Sep 12 2019 *)
%o (PARI) a006694(n)=sumdiv(2*n+1, d, eulerphi(d)/znorder(Mod(2, d))) - 1;
%o isok(n) = (n % 2) && (a006694((n-1)/2) == 3); \\ _Michel Marcus_, Feb 08 2016
%Y Cf. A006694, A002326, A001122, A001133.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Jun 15 2008
%E More terms from _Michel Marcus_, Feb 08 2016
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