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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..38.

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

Cf. A000032, A100107.

Sequence in context: A096305 A039888 A036959 * A280429 A076387 A193622

Adjacent sequences: A108028 A108029 A108030 * A108032 A108033 A108034

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 31 2005

STATUS

approved

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Last modified December 2 12:19 EST 2022. Contains 358493 sequences. (Running on oeis4.)