A108031 Inverse Moebius transform of Lucas numbers (A000032).
2, 3, 5, 7, 9, 17, 20, 36, 52, 86, 125, 220, 324, 542, 855, 1400, 2209, 3635, 5780, 9439, 15150, 24602, 39605, 64328, 103691, 168086, 271495, 439750, 710649, 1150794, 1860500, 3011749, 4870975, 7883406, 12752070, 20637077, 33385284, 54024302
Offset: 1
Keywords
Examples
a(4)=7 because the divisors of 4 are 1,2,4 and the first, second and fourth Lucas numbers are 2, 1 and 4, respectively, having sum 7.
Programs
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Maple
with(combinat): with(numtheory): f:=n->2*fibonacci(n)-fibonacci(n-1): g:=proc(n) local div: div:=divisors(n): sum(f(div[j]),j=1..tau(n)) end: seq(g(n),n=1..45);
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Mathematica
Table[Total[LucasL[#]&/@(Divisors[n]-1)],{n,40}] (* Harvey P. Dale, Dec 08 2014 *)
Formula
a(n) ~ phi^(n-1), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Dec 10 2021