A113486 a(n) = A113166(n) - Fibonacci(n-1), where Fibonacci(n) = A000045(n).

0, 0, 0, 1, 0, 3, 0, 4, 2, 7, 0, 13, 0, 14, 10, 21, 0, 39, 0, 52, 22, 65, 0, 137, 12, 156, 48, 267, 0, 483, 0, 652, 120, 1003, 50, 1849, 0, 2602, 300, 4329, 0, 7295, 0, 11086, 864, 17733, 0, 30125, 48, 46536, 1990, 75349, 0, 124683, 250, 197018, 5186, 317839, 0

Offset: 1

Author

Creighton Dement, Jan 09 2006; corrected Jun 20 2006

Keywords

• nonn

Comments

This sequence appears to be nonnegative. However, a proof of this has not yet been found.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A113166, A000045.

Programs

Mathematica

a[n_] := Sum[ k/(n - k)*Sum[ Binomial[(n - k)*GCD[n, k, j]/GCD[n, k],
k*GCD[n, k, j]/GCD[n, k]], {j, 1, GCD[n, k]}], {k, 1, Floor[n/2]}];
Table[a[n] - Fibonacci[n - 1], {n,1,50}] (* G. C. Greubel, Mar 12 2017 *)

Formula

For prime p, a(p) = 0 (see A113166 for details).

Extensions

More terms from R. J. Mathar, Feb 08 2008

More terms from Max Alekseyev, Jun 06 2009