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A007435 Inverse Moebius transform of Fibonacci numbers 1,1,2,3,5,8,...
(Formerly M0631)
8
1, 2, 3, 5, 6, 12, 14, 26, 37, 62, 90, 159, 234, 392, 618, 1013, 1598, 2630, 4182, 6830, 10962, 17802, 28658, 46548, 75031, 121628, 196455, 318206, 514230, 832722, 1346270, 2179322, 3524670, 5704486, 9227484, 14933129, 24157818, 39092352, 63246222, 102341006 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For p prime, a(p) == k (mod p) where k = 0 if p == 2, 3 (mod 5), k = 2 if p == 1, 4 (mod 5) and k = 1 if p = 5. - Michael Somos, Apr 15 2012

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

FORMULA

Row sums of A051731 * A127647. - Gary W. Adamson, Jan 22 2007

G.f.: Sum_{k>0} Fibonacci(k)*x^k/(1-x^k) = Sum_{k>0} x^k/(1-x^k-x^(2*k)). - Vladeta Jovovic, Dec 17 2002

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(Fibonacci(k)/k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 20 2018

a(n) ~ 5^(-1/2) * phi^n, where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, May 21 2018

EXAMPLE

x + 2*x^2 + 3*x^3 + 5*x^4 + 6*x^5 + 12*x^6 + 14*x^7 + 26*x^8 + 37*x^9 + 62*x^10 + ...

MATHEMATICA

Table[Plus @@ Map[Function[d, Fibonacci[d]], Divisors[n]], {n, 100}] (* T. D. Noe, Aug 14 2012 *)

a[n_] := DivisorSum[n, Fibonacci]; Array[a, 40] (* Jean-Fran├žois Alcover, Dec 01 2015 *)

PROG

(PARI) {a(n) = if( n<1, 0, sumdiv( n, k, fibonacci(k)))} /* Michael Somos, Apr 15 2012 */

CROSSREFS

Cf. A000045, A051731, A127647, A245282.

Sequence in context: A127525 A179333 A128958 * A125877 A118787 A191783

Adjacent sequences:  A007432 A007433 A007434 * A007436 A007437 A007438

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Added more terms, Joerg Arndt, Aug 14 2012.

STATUS

approved

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)