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%I #13 Jan 23 2024 15:46:35
%S 1,5,6,16,13,36,31,74,87,155,201,402,523,911,1398,2339,3573,5997,9351,
%T 15438,24546,40011,64081,104544,167786,272495,439372,712452,1149853,
%U 1863588,3010351,4875451,7881606,12759195,20633323,33397854,54018523,87422511,141423378
%N Inverse Moebius transform of A100107.
%C Or, the inverse Moebius transform of the inverse Moebius transform of the Lucas numbers A000032.
%F a(n) = Sum_{d|n} A100107(d).
%p 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);
%p # second Maple program:
%p a:= ((p-> j-> add(p(d), d=numtheory[divisors](j)))@@2)
%p (n-> (<<1|1>, <1|0>>^n.<<2, -1>>)[1, 1]):
%p seq(a(n), n=1..40); # _Alois P. Heinz_, Jan 23 2024
%t A100107[n_] := LucasL /@ Divisors[n] // Total;
%t a[n_] := A100107 /@ Divisors[n] // Total;
%t Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Jan 23 2024 *)
%Y Cf. A000032, A100107, A100279.
%K easy,nonn
%O 1,2
%A _R. J. Mathar_, Aug 21 2007
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