cp's OEIS Frontend

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.

%I A379543 #6 Jan 15 2025 23:51:20
%S A379543 2,1,8,14,24,69,84,76,59,179,195,159,314,449,384,984,467,359,909,744,
%T A379543 839
%N 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.
%C A379543 Warning: Do not confuse with the strict version A379843.
%e A379543 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}.
%t A379543 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A379543 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A379543 s=Table[Length[Select[Join@@Array[facs,n],Total[#]+Times@@#==n&]],{n,100}];
%t A379543 Table[Position[s,k-1][[1,1]],{k,mnrm[s+1]}]
%Y A379543 Positions of first appearances in A379669.
%Y A379543 For sets instead of multisets we have A379843, firsts of A379679.
%Y A379543 Arrays counting multisets by sum and product:
%Y A379543 - partitions: A379666, antidiagonal sums A379667
%Y A379543 - partitions without ones: A379668, antidiagonal sums A379669
%Y A379543 - strict partitions: A379671, antidiagonal sums A379672
%Y A379543 - strict partitions without ones: A379678, antidiagonal sums A379679.
%Y A379543 A000041 counts integer partitions, strict A000009.
%Y A379543 A001055 counts integer factorizations, strict A045778.
%Y A379543 A002865 counts partitions into parts > 1, strict A025147.
%Y A379543 A318950 counts factorizations by sum.
%Y A379543 Cf. A069016, A111133, A319000, A379670, A379680, A379720, A379839, A379840, A379841, A379842.
%K A379543 nonn,more
%O A379543 0,1
%A A379543 _Gus Wiseman_, Jan 15 2025