OFFSET
1,4
EXAMPLE
The a(6) = 7 pairs:
6 <= (6)
6 <= (4,2)
8 <= (4,2)
6 <= (3,3)
9 <= (3,3)
6 <= (2,2,2)
8 <= (2,2,2)
The a(7) = 9 pairs:
7 <= (7)
7 <= (5,2)
10 <= (5,2)
7 <= (4,3)
12 <= (4,3)
7 <= (3,2,2)
8 <= (3,2,2)
10 <= (3,2,2)
12 <= (3,2,2)
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[Total[Length/@nexos/@Select[IntegerPartitions[n], FreeQ[#, 1]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Oct 01 2018
STATUS
approved