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.
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, 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, 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
Offset: 5
Keywords
Examples
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.
Crossrefs
Cf. A008474.
Programs
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Mathematica
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]]