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%I #18 Nov 26 2020 03:17:35
%S 15,91,289,319,435,561,692,703,1016,1105,1369,1495,1729,1885,1891,
%T 2105,2465,2701,2755,2821,3367,4371,5551,6409,6601,7456,8224,8569,
%U 8695,8911,9088,10585,10621,11305,11849,12121,12403,13981,14065,15051,15841,16471,17104
%N Composite numbers k, not a power of 2, such that the E(k) == 1 (mod k), where E(k) is the k-th Euler number (A000364).
%t Select[Range[1000], CompositeQ[#] && #/2^IntegerExponent[#, 2] > 1 && Divisible[Abs[EulerE[2*#]] - 1, #] &] (* _Amiram Eldar_, Nov 26 2020 *)
%o (PARI) a000364(n)=subst(bernpol(2*n+1), 'x, 1/4)*4^(2*n+1)*(-1)^(n+1)/(2*n+1);
%o lista(nn) = {forcomposite(n=1, nn, if ( n != 2^valuation(n, 2), if (Mod(a000364(n), n) == 1, print1(n, ", "));););} \\ _Michel Marcus_, Apr 18 2015
%Y Cf. A000364, A081730.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Apr 06 2003
%E More terms from _Hans Havermann_, Apr 07 2003
%E a(23)-a(43) from _Amiram Eldar_, Nov 26 2020
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