A287273 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,...}.

6, 10, 19, 16, 24, 42, 71, 68, 106, 150, 178, 447, 288, 431, 3026, 754, 1119, 1220, 1902, 2974, 3194, 19979, 5168, 142026, 7728, 13098, 13530, 136187, 20276, 62158, 34130, 52994, 119811, 92736, 138673, 6169970, 241310, 6379215, 392836, 55946694, 587943, 768686

Offset: 1

Author

Michel Lagneau, May 22 2017

Keywords

• nonn

Comments

This sequence is included in A273227.

The primes of the sequence are 19, 71, 431, 19979,...

Examples

			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.
		

Crossrefs

Cf. A000045, A002808, A090206, A273227.

Programs

Mathematica

Function[n, Min@ Map[# + n/# &, Take[#, Ceiling[Length[#]/2]]] &@ Divisors@ n] /@ Select[Fibonacci@ Range@ 55, CompositeQ] (* Michael De Vlieger, May 24 2017 *)

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", ")).