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%I #50 Jul 22 2024 15:35:10
%S 1,2,6,18,42,54,126,162,294,342,378,486,882,1026,1134,1314,1458,1806,
%T 2058,2394,2646,3078,3402,3942,4374,5334,5418,6174,6498,7182,7938,
%U 9198,9234,10206,11826,12642,13122,14154,14406,16002,16254
%N Numbers k such that k divides 2^(k+1) - 2.
%C Also, numbers k such that k divides Eulerian number A000295(k+1) = 2^(k+1) - k - 2.
%C Also, numbers k such that k divides A086787(k) = Sum_{i=1..k} Sum_{j=1..k} i^j.
%C All terms greater than 1 are even; for a proof, see comment in A036236. - _Max Alekseyev_, Feb 03 2012
%C If k>1 is a term, then 3*k is also a term. - _Alexander Adamchuk_, Nov 03 2006
%C Prime numbers of the form a(m)+1 are given by A069051. - _Max Alekseyev_, Nov 14 2012
%C The number 2^m - 2 is a term of this sequence if and only if m - 1 is a term. - _Thomas Ordowski_, Jul 01 2024
%H Amiram Eldar, <a href="/A014741/b014741.txt">Table of n, a(n) for n = 1..10000</a>
%F For n > 1, a(n) = 2*A014945(n-1). - _Max Alekseyev_, Nov 14 2012
%t Join[{1,2},Select[Range[17000],PowerMod[2,#+1,#]==2&]] (* _Harvey P. Dale_, Feb 11 2015 *)
%o (PARI) is(n)=Mod(2,n)^(n+1)==2 \\ _Charles R Greathouse IV_, Nov 03 2016
%Y Cf. A000295, A086787, A015919, A006517, A330382.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, _Olivier Gérard_