OFFSET
1,2
COMMENTS
Or, the inverse Moebius transform of the inverse Moebius transform of the Lucas numbers A000032.
FORMULA
a(n) = Sum_{d|n} A100107(d).
MAPLE
A000032 := proc(n) option remember; if n =0 then 2; elif n = 1 then 1; else A000032(n-1)+A000032(n-2) ; fi ; end: A100107 := proc(n) option remember ; local a, dvs, d ; a := 0: dvs := numtheory[divisors](n) ; for d in dvs do a := a+ A000032(d) ; od: RETURN(a) ; end: a := proc(n) local a, dvs, d ; a := 0: dvs := numtheory[divisors](n) ; for d in dvs do a := a+ A100107(d) ; od: RETURN(a) ; end: seq(a(n), n=1..100);
# second Maple program:
a:= ((p-> j-> add(p(d), d=numtheory[divisors](j)))@@2)
(n-> (<<1|1>, <1|0>>^n.<<2, -1>>)[1, 1]):
seq(a(n), n=1..40); # Alois P. Heinz, Jan 23 2024
MATHEMATICA
A100107[n_] := LucasL /@ Divisors[n] // Total;
a[n_] := A100107 /@ Divisors[n] // Total;
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jan 23 2024 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
R. J. Mathar, Aug 21 2007
STATUS
approved