A063478 a(n) = Sum_{d|Fibonacci(n)} d^2.

1, 1, 5, 10, 26, 85, 170, 500, 1450, 3172, 7922, 31031, 54290, 143140, 483860, 1105000, 2550410, 8923300, 17494900, 53353040, 150655700, 313727044, 821223650, 3291697500, 5862907302, 14736586180, 48413209000, 113026206800

Offset: 1

Author

Jason Earls, Jul 28 2001

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1422 (terms 1..200 from Harry J. Smith)
• Florian Luca, Arithmetic Functions of Fibonacci Numbers, The Fibonacci Quarterly, Vol. 37, No. 3 (1999), pp. 265-268.

Crossrefs

Cf. A000045, A001157.

Programs

Mathematica

DivisorSigma[2,Fibonacci[Range[30]]] (* Harvey P. Dale, Jul 05 2021 *)

PARI

j=[]; for(n=1,40,j=concat(j,sumdiv(fibonacci(n),d,d^2))); j

PARI

{ allocatemem(20000000); h=1; g=f=0; for (n=1, 200, f+=h; h=g; g=f; write("b063478.txt", n, " ", sumdiv(f, d, d^2)) ) } \\ Harry J. Smith, Aug 23 2009

Sage

[sigma(fibonacci(n),2)for n in range(1,29)] # Zerinvary Lajos, Jun 04 2009

Formula

From Amiram Eldar, Jan 12 2022: (Start)

a(n) = A001157(A000045(n)).

a(n) <= A000045(A001157(n)), with equality if and only if n = 1 (Luca, 1999). (End)