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%I #12 Dec 07 2015 03:52:54
%S 21,35,45,51,65,69,75,77,85,91,93,99,105,115,117,123,129,133,141,145,
%T 147,155,165,171,185,187,189,195,203,205,213,215,217,219,221,231,235,
%U 237,245,247,253,255,259,261,265,267,273,275,279,285,291,299,301,305
%N Odd positive integers n for which A137576((n-1)/2)-1 is not a multiple of A000010(n).
%C All terms are composite numbers since if p is an odd prime then A137576((p-1)/2)-1=p-1=A000010(p).
%C Conjecture. This sequence is infinite.
%H Ray Chandler, <a href="/A138227/b138227.txt">Table of n, a(n) for n = 1..6500</a>
%t A137576[n_] := With[{t = MultiplicativeOrder[2, 2 n + 1]}, t*DivisorSum[2 n + 1, EulerPhi[#]/MultiplicativeOrder[2, #] &] - t + 1]; Select[Range[1, 1000, 2], !Divisible[A137576[(# - 1)/2] - 1, EulerPhi[#]]&] (* _Jean-François Alcover_, Dec 07 2015 *)
%o (PARI) is(n)=my(t); n%2 && (sumdiv(n,d,eulerphi(d)/(t=znorder(Mod(2, d))))*t-t)%eulerphi(n)>0 \\ _Charles R Greathouse IV_, Feb 20 2013
%Y Cf. A137576, A000010, A002326, A006694.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, May 05 2008
%E Extended by _Ray Chandler_, May 08 2008
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