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A108031
Inverse Moebius transform of Lucas numbers (A000032).
0
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
1,1
FORMULA
a(n) ~ phi^(n-1), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Dec 10 2021
EXAMPLE
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.
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);
MATHEMATICA
Table[Total[LucasL[#]&/@(Divisors[n]-1)], {n, 40}] (* Harvey P. Dale, Dec 08 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 31 2005
STATUS
approved