The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319907 Number of distinct integers that can be obtained by iteratively adding any two or multiplying any two non-1 parts of an integer partition until only one part remains, starting with the integer partition with Heinz number n. 0
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 4, 1, 2, 2, 1, 2, 4, 1, 1, 2, 4, 1, 4, 1, 2, 4, 1, 1, 4, 2, 3, 2, 2, 1, 5, 2, 4, 2, 1, 1, 5, 1, 1, 4, 4, 2, 4, 1, 2, 2, 4, 1, 5, 1, 1, 6, 2, 2, 4, 1, 5, 4, 1, 1, 7, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,15 COMMENTS The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). LINKS EXAMPLE The Heinz number of (3,3,2) is 75 and we have     3+3+2 = 8,     3+3*2 = 9,     3*3+2 = 11,   (3+3)*2 = 12,   3*(3+2) = 15,     3*3*2 = 18, so a(75) = 6. MATHEMATICA ReplaceListRepeated[forms_, rerules_]:=Union[Flatten[FixedPointList[Function[pre, Union[Flatten[ReplaceList[#, rerules]&/@pre, 1]]], forms], 1]]; mexos[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_?(#>1&), mie___, y_?(#>1&), afe___}:>Sort[Append[{foe, mie, afe}, x*y]]}], Length[#]==1&]]; Table[Length[mexos[If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]], {n, 100}] CROSSREFS Cf. A000792, A001970, A005520, A048249, A066739, A070960, A201163, A275870, A319850, A318949, A319855, A319856, A319909, A319912, A319913. Sequence in context: A109374 A079706 A250005 * A078703 A090629 A248623 Adjacent sequences:  A319904 A319905 A319906 * A319908 A319909 A319910 KEYWORD nonn AUTHOR Gus Wiseman, Oct 01 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 16 10:51 EDT 2021. Contains 343037 sequences. (Running on oeis4.)