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%I #6 May 28 2017 09:47:54
%S 6,10,19,16,24,42,71,68,106,150,178,447,288,431,3026,754,1119,1220,
%T 1902,2974,3194,19979,5168,142026,7728,13098,13530,136187,20276,62158,
%U 34130,52994,119811,92736,138673,6169970,241310,6379215,392836,55946694,587943,768686
%N Consider all ways of writing the composite Fibonacci number A090206(n+3) as product of two divisors d1*d2 = d3*d4 = ... The sequence a(n) gives the minimum sums of {d1+d2, d3+d4,...}.
%C This sequence is included in A273227.
%C The primes of the sequence are 19, 71, 431, 19979,...
%e a(5) = 24 because A090206(8) = 144 = 1*144 = 2*72 = 3*48 = 4*36 = 6*24 = 8*18 = 9*16 = 12*12 and the minimum sum of {145, 74, 51, 40, 30, 26, 25, 24} is 24.
%t Function[n, Min@ Map[# + n/# &, Take[#, Ceiling[Length[#]/2]]] &@ Divisors@ n] /@ Select[Fibonacci@ Range@ 55, CompositeQ] (* _Michael De Vlieger_, May 24 2017 *)
%o (PARI) for(n=1, 100, d=divisors(fibonacci(n)); t=#d; k=if(t%2, 2*d[t\2+1], d[t\2]+d[t\2+1]); print1(k", ")).
%Y Cf. A000045, A002808, A090206, A273227.
%K nonn
%O 1,1
%A _Michel Lagneau_, May 22 2017
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