A379543 Least number x such that there are exactly n multisets of positive integers > 1 with sum + product = x. Position of first appearance of n in A379669.

2, 1, 8, 14, 24, 69, 84, 76, 59, 179, 195, 159, 314, 449, 384, 984, 467, 359, 909, 744, 839

Offset: 0

Author

Gus Wiseman, Jan 15 2025

Keywords

• nonn
• more

Comments

Warning: Do not confuse with the strict version A379843.

Examples

			We have a(5) = 69 due to the following five multisets: {4,13}, {6,9}, {2,2,13}, {2,4,7}, {2,2,2,7}.
		

Crossrefs

Positions of first appearances in A379669.

For sets instead of multisets we have A379843, firsts of A379679.

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, A379670, A379680, A379720, A379839, A379840, A379841, A379842.

Programs

Mathematica

facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[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[facs,n],Total[#]+Times@@#==n&]],{n,100}];
Table[Position[s,k-1][[1,1]],{k,mnrm[s+1]}]