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A217738 Numbers k such that Fibonacci(k) is divisible by k*(k+1).

%I A217738 #17 Mar 24 2021 09:52:30
%S A217738 60,108,180,240,540,600,660,768,1008,1200,1320,1620,1800,1860,2160,
%T A217738 2520,2688,2736,3000,3060,3300,3360,3528,3888,4200,4800,4860,4968,
%U A217738 5280,5520,5580,5880,6120,6480,6600,6720,6840,7320,7560,7680,8100,8208,8640,9000,9180,9240,9600
%N A217738 Numbers k such that Fibonacci(k) is divisible by k*(k+1).
%C A217738 Indices of 0's in A217737.
%C A217738 Conjectures: the sequence is infinite; all terms are divisible by 12.
%H A217738 Alois P. Heinz, <a href="/A217738/b217738.txt">Table of n, a(n) for n = 1..1000</a> (first 370 terms from Harvey P. Dale)
%t A217738 Select[Range[10000],Divisible[Fibonacci[#],#(#+1)]&] (* _Harvey P. Dale_, Aug 14 2014 *)
%o A217738 (Python)
%o A217738 prpr, prev = 0, 1
%o A217738 for i in range(1, 1000):
%o A217738     cur = prpr + prev
%o A217738     a = prev % (i*(i+1))
%o A217738     if a==0:
%o A217738       print(str(i), end=', ')
%o A217738     prpr, prev = prev, cur
%Y A217738 Cf. A000045, A002378, A217737.
%K A217738 nonn
%O A217738 1,1
%A A217738 _Alex Ratushnyak_, Mar 22 2013