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Block[{a, b, nn = 1122}, a = Min@ Map[Total, #] & /@ Nest[Function[{a, n}, Append[a, Join @@ Table[Flatten@ Prepend[#, n] & /@ a[[n - n/p]], {p, FactorInteger[n][[All, 1]]}]]] @@ {#, Length@ # + 1} &, {{{1}}}, nn]; b = Array[If[# == 1, 1, Total@ NestWhileList[If[PrimeQ@ #, # - 1, # - #/FactorInteger[#][[1, 1]] ] &, #, # > 1 &]] &, nn]; Select[Range@ nn, a[[#]] < b[[#]] &]] (* Michael De Vlieger, Apr 15 2020 *)

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Numbers n for which the {smallest path sum when iterating from n to 1 with nondeterministic map k -> k - k/p, where p is any prime factor of k} cannot be obtained by always selecting the smallest prime factor of k (A020639). See the example in A333790 how that simple heuristics heuristic fails when starting from k=119.

Numbers n for which the {smallest path sum when iterating from n to 1 with nondeterministic map k -> k - k/p, where p is any prime factor of k} cannot be obtained by always selecting the smallest prime factor of k (A020639). See the example in A333790 how that simple heuristic heuristics fails when starting from k=119.

Numbers n for which the {smallest path sum when iterating from n to 1 with nondeterministic map k -> k - k/p, where p is any prime factor of k, } cannot be obtained by always selecting the smallest prime factor of k (A020639). See the example in A333790 how that simple heuristic fails when starting from k=119.

Numbers n for which the smallest path sum when iterating from n to 1 with nondeterministic map k -> k - k/p, where p is any prime factor of k, cannot be obtained by always selecting the smallest prime factor of k (A020639). See the example in A333790 how that simple heuristic fails, when starting from k=119.