A108031 - OEIS

A108031

Inverse Moebius transform of Lucas numbers (A000032).

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

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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, A001622, 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