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%I #28 Sep 08 2022 08:46:14
%S 1,60,240,600,660,768,1008,1200,1320,1800,1860,2160,2688,2736,3000,
%T 3300,3360,3888,4620,4800,5280,5520,5568,6120,6480,6720,6840,7320,
%U 7680,8208,8640,9000,9600,9720,10368,11160,12240,12288,13200,13248,13440,13680,13868,14400,15120,15360
%N Positive values of n such that A027961(n) is divisible by A000217(n).
%C Is there a maximum value of a(n) - a(n-1)?
%C A263161 is not a subsequence although they have many common terms.
%C Terms that are not congruent to 0 (mod 6): 1, 13868, 16016, 34988, 158252, 196412, 313988, 1287788, 2056748, 2212412, 2542028, 2847260, 2951708, 6117548, 7538108, 7756988, 9056732, 9865628, ... . - _Robert G. Wilson v_, Oct 15 2015
%e For n = 1, A027961(1) = 1 is divisible by A000217(1) = 1.
%e For n = 60, A027961(60) = 9062201101800 = 1830*4952022460, therefore it is divisible by A000217(60) = 1830.
%t fQ[n_] := Mod[ Fibonacci[n + 1] + Fibonacci[n + 3] - 3, n (n + 1)/2] == 0; Select[ Range@ 16000, fQ] (* _Robert G. Wilson v_, Oct 15 2015 *)
%o (PARI) for(n=1, 20000, if((fibonacci(n+3) + fibonacci(n+1)-3) % (n*(n+1)/2) == 0, print1(n", ")));
%o (Magma) [n: n in [1..20000] | IsDivisibleBy(Lucas(n+2)-3,n*(n+1) div 2)]; // _Bruno Berselli_, Oct 19 2015
%Y Cf. A000204, A000217, A027961, A263161.
%K nonn,easy
%O 1,2
%A _Altug Alkan_, Oct 12 2015