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%I #7 May 18 2024 01:49:36
%S 1,2,4,8,16,32,64,68,128,256,512,592,1024,1156,2048,2056,4096,4112,
%T 8192,8224,8576,10928,16384,16448,19652,20512,28936,32768,37888,41024,
%U 43882,64804,65536,82048
%N Numbers k that divide the k-th tangent (or "zag") number.
%C Numbers k such that k | A000182(k).
%C All the powers of 2 are terms.
%e 2 is a term since A000182(2) = 2 is divisible by 2.
%e 4 is a term since A000182(4) = 272 = 4 * 68 is divisible by 4.
%t Select[Range[1000], Divisible[((-4)^# - (-16)^#) * BernoulliB[2*#]/(2*#), #] &]
%o (PARI) is(n) = (((-4)^n - (-16)^n) * bernfrac(2*n) / (2*n)) % n == 0;
%Y Cf. A000182.
%Y Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).
%K nonn,more
%O 1,2
%A _Amiram Eldar_, May 17 2024