A119737 a(n) = Sum{k=1..n} Fibonacci(floor(n/k)).

1, 2, 4, 6, 9, 14, 20, 30, 45, 69, 104, 165, 255, 405, 642, 1029, 1640, 2645, 4243, 6852, 11040, 17840, 28787, 46567, 75227, 121685, 196725, 318269, 514688, 832760, 1346990, 2179417, 3525722, 5704642, 9229228, 14933176, 24160642, 39092592

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Formula

a(n) also equals n + sum{k=1..n-2} Fibonacci(k) floor(n/(k+2)), for n >= 2.

Mathematica

f[n_] := Sum[ Fibonacci@Floor[n/k], {k, n}] (* or *) f[n_] := n + Sum[Fibonacci@k*Floor[n/(k + 2)], {k, n - 2}]; Array[f, 38] (* Robert G. Wilson v *)

Crossrefs

Cf. A000045.

Sequence in context: A139135 A097197 A260600 * A038718 A042942 A256968

Adjacent sequences: A119734 A119735 A119736 * A119738 A119739 A119740

Keyword

easy,nonn

Author

Leroy Quet, Jun 15 2006

Extensions

More terms from Robert G. Wilson v and Joshua Zucker, Jun 19 2006

Status

approved