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A109496 a(n) is the first integer k for which b(b(...b(n)...))=5, where the transformation b(m), the m-th term of A008474, is taken k-1 times. 0

%I #1 Sep 21 2005 03:00:00

%S 1,4,3,2,2,3,4,3,6,5,4,5,4,3,5,4,4,5,4,3,4,5,5,4,8,7,5,4,6,5,6,3,6,5,

%T 4,5,6,5,7,6,5,6,5,4,3,4,6,4,4,3,4,7,4,7,7,6,8,7,7,3,5,6,7,6,5,5,5,4,

%U 8,7,5,4,5,5,5,4,4,6,7,6,4,6,6,5,7,6,6,5,4,7,6,5,5,4,5,5,6,5,7,6,4,5,5,4,6

%N a(n) is the first integer k for which b(b(...b(n)...))=5, where the transformation b(m), the m-th term of A008474, is taken k-1 times.

%e a(6)=4 because b(6=2^1*3^1)=7, b(7=7^1)=8, b(8=2^3)=5, so we apply b(m) 3 times to get 5.

%t f[n_] := Sum[FactorInteger[n][[i]][[1]] + FactorInteger[n][[i]][[2]], { i, Length[FactorInteger[n]]}] g[t_, n_] := If[t == 1, n, f[g[t - 1, n]]]; a[n_] := Position[Array[g[ #, n] &, 100], 5, {1}, 1][[1, 1]]

%Y Cf. A008474.

%K nonn

%O 5,2

%A Y. Kallus (yoav(AT)rice.edu), Aug 29 2005

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