%I #14 Sep 21 2017 10:11:06

%S 1,9,19313,226703,345023,673663,929783,1697609,1790159,1878073,

%T 2391991,3441743,8026103,9520441,9770153,10751841,30652223,35482433,

%U 40642103,41839231,50358247,57233047,65046479,69601193,85246441,110944089,117368839,119611073,122527433

%N Odd numbers n such that 2^d(n) == 2^n (mod n) where d = A000005.

%C Square terms are 1, 3^2, 3^2*1093^2, 3^2*3511^2 and there are no other squares k^2 with k < 3*10^9. Note that 1093 and 3511 are Wieferich primes (A001220). - _Giovanni Resta_, Sep 19 2017

%e 19313 = 7*31*89 is a term because d(19313) = 2^3 and 7*31*89 divides 2^(7*31*89) - 2^8.

%t Select[Range[1, 10^7, 2], PowerMod[2, DivisorSigma[0, #], #] == PowerMod[2, #, #] &] (* _Michael De Vlieger_, Sep 19 2017 *)

%o (PARI) isok(n) = n%2==1 && Mod(2, n)^n==2^numdiv(n);

%Y Cf. A000005.

%K nonn

%O 1,2

%A _Altug Alkan_, Sep 19 2017