A123339 a(1)=1. For n >= 2, a(n) = Sum_{k=1..(n-1)} k^b(a(n-k),k), where k^b(m,k) is the highest power of k that divides m (and where b(m,k) is a nonnegative integer).

1, 1, 2, 3, 5, 5, 8, 7, 15, 13, 17, 13, 12, 17, 30, 17, 20, 19, 26, 23, 29, 25, 34, 37, 57, 25, 59, 45, 28, 43, 81, 43, 55, 113, 34, 41, 82, 41, 39, 135, 40, 43, 124, 71, 108, 49, 76, 73, 69, 77, 121, 81, 100, 61, 151, 55, 136, 107, 65, 59, 212, 181, 181, 67, 74, 83, 103, 67

Offset

0,3

Comments

1^b(m,1) is considered here to be 1 for all m.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Example

The highest power of 1 dividing a(6) is 1. The highest power of 2 dividing a(5) is 1. The highest power of 3 dividing a(4) is 3. The highest power of 4 dividing a(3) is 1. The highest power of 5 dividing a(2) is 1. And the highest power of 6 dividing a(1) is 1. So a(7) = 1+1+3+1+1+1 = 8.

Mathematica

b[m_, k_] := If[k == 1, 1, IntegerExponent[m, k]]; f[l_List] := Append[l, Sum[k^b[l[[Length[l] + 1 - k]], k], {k, Length[l]}]]; Nest[f, {1}, 70] (* Ray Chandler, Oct 17 2006 *)

Crossrefs

Sequence in context: A208323 A067284 A353272 * A246104 A256654 A204926

Adjacent sequences: A123336 A123337 A123338 * A123340 A123341 A123342

Keyword

nonn

Author

Leroy Quet, Oct 11 2006

Extensions

Extended by Ray Chandler, Oct 17 2006

Status

approved