A130878 Inverse Moebius transform of A100107.

1, 5, 6, 16, 13, 36, 31, 74, 87, 155, 201, 402, 523, 911, 1398, 2339, 3573, 5997, 9351, 15438, 24546, 40011, 64081, 104544, 167786, 272495, 439372, 712452, 1149853, 1863588, 3010351, 4875451, 7881606, 12759195, 20633323, 33397854, 54018523, 87422511, 141423378

Offset: 1

Author

R. J. Mathar, Aug 21 2007

Keywords

• easy
• nonn

Comments

Or, the inverse Moebius transform of the inverse Moebius transform of the Lucas numbers A000032.

Crossrefs

Cf. A000032, A100107, A100279.

Programs

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 *)

Formula

a(n) = Sum_{d|n} A100107(d).