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A263578 Positive values of k such that A014286(k) is divisible by k. 0

%I #15 Nov 25 2015 02:30:52

%S 1,3,18,24,42,48,72,96,120,138,144,192,216,240,258,264,282,288,336,

%T 360,384,402,432,480,498,576,600,618,642,648,672,714,720,744,762,768,

%U 864,912,960,978,1002,1008,1080,1104,1152,1200,1224,1296,1320,1338,1344,1362

%N Positive values of k such that A014286(k) is divisible by k.

%C Sequence is interesting because of the values of a(n) - a(n-1). For a(n) < 10000, the most common repeated values of a(n) - a(n-1) are 24 and 6. Will this situation continue?

%e a(2) = 3 because Fibonacci(1) + 2 * Fibonacci(2) + 3 * Fibonacci(3) = 9, which is divisible by 3.

%t Select[Range@ 1584, Divisible[Sum[i Fibonacci@ i, {i, 0, #}], #] &] (* _Michael De Vlieger_, Oct 22 2015 *)

%o (PARI) for(n=1, 2000, if(sum(k=1, n, k*fibonacci(k)) % n == 0, print1(n, ", ")))

%Y Cf. A000045, A014286.

%K nonn,easy

%O 1,2

%A _Altug Alkan_, Oct 22 2015

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Last modified April 21 01:42 EDT 2024. Contains 371850 sequences. (Running on oeis4.)