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A113222 a(n) = sum{p=primes, p|n} F(p^(m_{n,p})), where p^(m_{n,p}) is highest power of p dividing n, m= nonnegative integer and F(k) is the k-th Fibonacci number. 2
0, 1, 2, 3, 5, 3, 13, 21, 34, 6, 89, 5, 233, 14, 7, 987, 1597, 35, 4181, 8, 15, 90, 28657, 23, 75025, 234, 196418, 16, 514229, 8, 1346269, 2178309, 91, 1598, 18, 37, 24157817, 4182, 235, 26, 165580141, 16, 433494437, 92, 39, 28658, 2971215073, 989 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..48.

FORMULA

Additive with a(p^e) = F(p^e).

EXAMPLE

12 = 2^2 * 3^1. So a(12) = F(2^2) + F(3^1) = 3 + 2 = 5.

MATHEMATICA

f[n_] := Plus @@ (Fibonacci[ #[[1]]^#[[2]]] & /@ FactorInteger[n]); Table[ f[n], {n, 49}] (* Robert G. Wilson v *)

CROSSREFS

Cf. A113195.

Sequence in context: A272202 A244609 A209195 * A060444 A002587 A152814

Adjacent sequences:  A113219 A113220 A113221 * A113223 A113224 A113225

KEYWORD

nonn

AUTHOR

Leroy Quet, Oct 18 2005

EXTENSIONS

More terms from Robert G. Wilson v, Oct 21 2005

STATUS

approved

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Last modified November 26 08:23 EST 2022. Contains 358354 sequences. (Running on oeis4.)