cp's OEIS Frontend

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.

%I A379843 #6 Jan 15 2025 23:51:16
%S A379843 2,1,14,44,47,89,119,179,159,239,335,539,599,744,359,719,839
%N 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.
%C A379843 Warning: Do not confuse with the multiset version A379543.
%e A379843 We have a(4) = 47 due to the following four sets: {5,7}, {2,15}, {3,11}, {2,3,6}.
%t A379843 nn=100;
%t A379843 strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A379843 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A379843 s=Table[Length[Select[Join@@Array[strfacs,n],Total[#]+Times@@#==n&]],{n,nn}];
%t A379843 Table[Position[s,k-1][[1,1]],{k,mnrm[s+1]}]
%Y A379843 For multisets instead of sets we have A379543, firsts of A379669.
%Y A379843 Positions of first appearances in A379679, see A379842.
%Y A379843 Arrays counting multisets by sum and product:
%Y A379843 - partitions: A379666, antidiagonal sums A379667
%Y A379843 - partitions without ones: A379668, antidiagonal sums A379669
%Y A379843 - strict partitions: A379671, antidiagonal sums A379672
%Y A379843 - strict partitions without ones: A379678, antidiagonal sums A379679.
%Y A379843 A000041 counts integer partitions, strict A000009.
%Y A379843 A001055 counts integer factorizations, strict A045778.
%Y A379843 A002865 counts partitions into parts > 1, strict A025147.
%Y A379843 A318950 counts factorizations by sum.
%Y A379843 Cf. A069016, A111133, A319000, A319057, A379670, A379680, A379720, A379839, A379840, A379841.
%K A379843 nonn,more
%O A379843 0,1
%A A379843 _Gus Wiseman_, Jan 15 2025