A379843 Least number x such that there are exactly n sets of positive integers > 1 with sum + product = x. Position of first appearance of n in A379679.

2, 1, 14, 44, 47, 89, 119, 179, 159, 239, 335, 539, 599, 744, 359, 719, 839

Offset: 0

Author

Gus Wiseman, Jan 15 2025

Keywords

• nonn
• more

Comments

Warning: Do not confuse with the multiset version A379543.

Examples

			We have a(4) = 47 due to the following four sets: {5,7}, {2,15}, {3,11}, {2,3,6}.
		

Crossrefs

For multisets instead of sets we have A379543, firsts of A379669.

Positions of first appearances in A379679, see A379842.

Arrays counting multisets by sum and product:

- partitions: A379666, antidiagonal sums A379667

- partitions without ones: A379668, antidiagonal sums A379669

- strict partitions: A379671, antidiagonal sums A379672

- strict partitions without ones: A379678, antidiagonal sums A379679.

A000041 counts integer partitions, strict A000009.

A001055 counts integer factorizations, strict A045778.

A002865 counts partitions into parts > 1, strict A025147.

A318950 counts factorizations by sum.

Cf. A069016, A111133, A319000, A319057, A379670, A379680, A379720, A379839, A379840, A379841.

Programs

Mathematica

nn=100;
strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
s=Table[Length[Select[Join@@Array[strfacs,n],Total[#]+Times@@#==n&]],{n,nn}];
Table[Position[s,k-1][[1,1]],{k,mnrm[s+1]}]