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%I #9 Mar 08 2023 13:40:21
%S 2,3,5,7,9,17,20,36,52,86,125,220,324,542,855,1400,2209,3635,5780,
%T 9439,15150,24602,39605,64328,103691,168086,271495,439750,710649,
%U 1150794,1860500,3011749,4870975,7883406,12752070,20637077,33385284,54024302
%N Inverse Moebius transform of Lucas numbers (A000032).
%F a(n) ~ phi^(n-1), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Dec 10 2021
%e 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.
%p 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);
%t Table[Total[LucasL[#]&/@(Divisors[n]-1)],{n,40}] (* _Harvey P. Dale_, Dec 08 2014 *)
%Y Cf. A000032, A001622, A100107.
%K nonn
%O 1,1
%A _Emeric Deutsch_, May 31 2005