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A379842 Numbers that are the sum + product of a unique set of positive integers > 1. Positions of 1 in A379679.

%I A379842 #6 Jan 16 2025 08:47:54
%S A379842 1,4,6,8,10,11,12,16,17,18,19,22,24,27,28,30,31,33,36,42,43,46,48,49,
%T A379842 52,58,61,63,66,67,70,73,85,88,91,97,100,102,105,108,115,126,130,141,
%U A379842 145,147,148,162,171,178,192,205,211,213,226,262,277,283,288,291
%N A379842 Numbers that are the sum + product of a unique set of positive integers > 1. Positions of 1 in A379679.
%e A379842 For sum + product = 29 we have two possibilities: {2,9} and {4,5}, so 29 is not in the sequence.
%e A379842 For sum + product = 33 we have only {2,3,4}, so 33 is in the sequence.
%t A379842 nn=100;
%t A379842 strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A379842 Join@@Position[Table[Length[Select[Join@@Array[strfacs,n],Total[#]+Times@@#==n&]],{n,nn}],1]
%Y A379842 Positions of 1 in A379679, see A379843.
%Y A379842 For at least one multiset we have A379839, complement A379670.
%Y A379842 For multisets instead of sets we have A379840.
%Y A379842 For at least one (instead of exactly one) we have A379841, complement A379680.
%Y A379842 Arrays counting multisets by sum and product:
%Y A379842 - partitions: A379666, antidiagonal sums A379667
%Y A379842 - partitions without ones: A379668, antidiagonal sums A379669
%Y A379842 - strict partitions: A379671, antidiagonal sums A379672
%Y A379842 - strict partitions without ones: A379678, antidiagonal sums A379679.
%Y A379842 A000041 counts integer partitions, strict A000009.
%Y A379842 A001055 counts integer factorizations, strict A045778.
%Y A379842 A002865 counts partitions into parts > 1, strict A025147.
%Y A379842 A318950 counts factorizations by sum.
%Y A379842 A326622 counts factorizations with integer mean, strict A328966.
%Y A379842 Cf. A069016, A111133, A319000, A319057, A326152, A326178, A379720.
%K A379842 nonn
%O A379842 1,2
%A A379842 _Gus Wiseman_, Jan 14 2025