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 A319856 Maximum number that can be obtained by iteratively adding or multiplying together parts of the integer partition with Heinz number n until only one part remains. 4
 0, 1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 6, 5, 6, 4, 7, 6, 8, 6, 8, 6, 9, 6, 9, 7, 8, 8, 10, 9, 11, 6, 10, 8, 12, 9, 12, 9, 12, 9, 13, 12, 14, 10, 12, 10, 15, 9, 16, 12, 14, 12, 16, 12, 15, 12, 16, 11, 17, 12, 18, 12, 16, 9, 18, 15, 19, 14, 18, 16, 20, 12, 21, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). LINKS EXAMPLE a(30) = 9 because the maximum number that can be obtained starting with (3,2,1) is 3*(2+1) = 9. MATHEMATICA ReplaceListRepeated[forms_, rerules_]:=Union[Flatten[FixedPointList[Function[pre, Union[Flatten[ReplaceList[#, rerules]&/@pre, 1]]], forms], 1]]; nexos[ptn_]:=If[Length[ptn]==0, {0}, Union@@Select[ReplaceListRepeated[{Sort[ptn]}, {{foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x+y]], {foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x*y]]}], Length[#]==1&]]; Table[Max[nexos[If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]], {n, 100}] CROSSREFS Cf. A000792, A001970, A048249, A056239, A066739, A066815, A070960, A201163, A319850, A318948, A318949, A319841, A319855. Sequence in context: A302039 A056239 A161511 * A100197 A057022 A287896 Adjacent sequences:  A319853 A319854 A319855 * A319857 A319858 A319859 KEYWORD nonn AUTHOR Gus Wiseman, Sep 29 2018 STATUS approved

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Last modified July 25 13:05 EDT 2021. Contains 346290 sequences. (Running on oeis4.)