A113178 a(n) = Sum_{p|n} F(p), where F(p) is the p-th Fibonacci number and where the sum is over the distinct prime divisors of n.
0, 1, 2, 1, 5, 3, 13, 1, 2, 6, 89, 3, 233, 14, 7, 1, 1597, 3, 4181, 6, 15, 90, 28657, 3, 5, 234, 2, 14, 514229, 8, 1346269, 1, 91, 1598, 18, 3, 24157817, 4182, 235, 6, 165580141, 16, 433494437, 90, 7, 28658, 2971215073, 3, 13, 6, 1599, 234
Offset: 1
Examples
12 = 2^2 * 3^1, so a(12) = F(2) + F(3) = 1 + 2 = 3.
Links
- Danny Rorabaugh, Table of n, a(n) for n = 1..4000
Programs
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Mathematica
b[t_]:=Fibonacci[First[t]] a[n_]:=Apply[Plus, Map[b, FactorInteger[n]]] (* Esa Peuha, Oct 26 2005 *)
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Sage
[0]+[sum([fibonacci(p) for p in prime_factors(n)]) for n in range(2,53)] # Danny Rorabaugh, Apr 03 2015
Formula
Additive with a(p^e) = F(p).
Extensions
More terms from Esa Peuha (esa.peuha(AT)helsinki.fi), Oct 26 2005