%I #28 Jan 03 2017 02:40:18
%S 1,2,5,17,91,379,5047,35849,614893,6800951,607326679,3651532639,
%T 851897554247,24724573280923,301787157353771,14188276949397301,
%U 22662903194758542865,430644772287132696121,1800653989272587268758525
%N Numerator of 1/F(1) + 1/F(2) + 1/F(3) + ... + 1/F(n), where F(n) is the n-th Fibonacci number (A000045).
%H G. C. Greubel, <a href="/A059248/b059248.txt">Table of n, a(n) for n = 1..100</a>
%H Naim Tuglu, Can Kizilates, Seyhun Kesim, <a href="http://arxiv.org/abs/1505.04284">On the Harmonic and Hyperharmonic Fibonacci Numbers</a>, arXiv:1505.04284 [math.NT], 2015 (see Table 1).
%e a(4) = 17 because 1/F1 + 1/F2 + 1/F3 + 1/F4 = 1 + 1 + 1/2 + 1/3 = 17/6 and the numerator is 17.
%e 1, 2, 5/2, 17/6, 91/30, 379/120, 5047/1560, 35849/10920, 614893/185640, 6800951/2042040, 607326679/181741560, ... = A059248/A035105.
%p BB:=n->sum(1/fibonacci(i), i=1..n): a:=n->floor(numer(BB(n))): seq(a(n), n=1..19); # _Zerinvary Lajos_, Mar 28 2007
%t Table[ 1 / Fibonacci[n], {n, 1, 19}] // Accumulate // Numerator (* _Jean-François Alcover_, Mar 07 2013 *)
%o (PARI) lista(nn) = s = 0; for (n=1, nn, s += 1/fibonacci(n); print1(numerator(s), ", ");); \\ _Michel Marcus_, Nov 28 2014
%Y Cf. A000045, A035105, Cf. A059246/A059247.
%K nonn,easy,frac
%O 1,2
%A Avi Peretz (njk(AT)netvision.net.il), Jan 22 2001
%E More terms from _Naohiro Nomoto_, Jun 21 2001
%E Offset changed to 1 by _Michel Marcus_, Nov 28 2014