A123339 - OEIS

%I #12 Oct 11 2019 12:32:38

%S 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,

%T 25,59,45,28,43,81,43,55,113,34,41,82,41,39,135,40,43,124,71,108,49,

%U 76,73,69,77,121,81,100,61,151,55,136,107,65,59,212,181,181,67,74,83,103,67

%N 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).

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

%H G. C. Greubel, <a href="/A123339/b123339.txt">Table of n, a(n) for n = 0..1000</a>

%e 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.

%t 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 *)

%K nonn

%O 0,3

%A _Leroy Quet_, Oct 11 2006

%E Extended by _Ray Chandler_, Oct 17 2006