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A379841 Numbers that are the sum + product of some set of positive integers > 1. Positions of nonzeros in A379679.

%I A379841 #5 Jan 09 2025 14:59:11
%S A379841 1,4,6,8,10,11,12,14,16,17,18,19,20,22,23,24,26,27,28,29,30,31,32,33,
%T A379841 34,35,36,38,39,40,41,42,43,44,46,47,48,49,50,51,52,53,54,55,56,58,59,
%U A379841 60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78
%N A379841 Numbers that are the sum + product of some set of positive integers > 1. Positions of nonzeros in A379679.
%e A379841 For sum + product = 14 we have two possibilities: {7} or {2,4}; so 14 is in the sequence.
%t A379841 nn=100;
%t A379841 strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A379841 Intersection[Range[nn],Total[#]+Times@@#&/@Join@@Array[strfacs,nn]]
%Y A379841 The version allowing 1's is A326178.
%Y A379841 Positions of nonzeros in A379679.
%Y A379841 The complement is A379680.
%Y A379841 The non-strict version is A379839, complement A379670.
%Y A379841 For unique (instead of some) we have A379842.
%Y A379841 Arrays counting multisets by sum and product: A379666, A379671, A379678.
%Y A379841 Counting and ranking multisets by comparing sum and product:
%Y A379841 - same: A001055 (strict A045778), ranks A301987
%Y A379841 - divisible: A057567, ranks A326155
%Y A379841 - divisor: A057568, ranks A326149, see A326156, A326172, A379733
%Y A379841 - greater: A096276 shifted right, ranks A325038
%Y A379841 - greater or equal: A096276, ranks A325044
%Y A379841 - less: A114324, ranks A325037, see A318029
%Y A379841 - less or equal: A319005, ranks A379721
%Y A379841 - different: A379736, ranks A379722, see A111133
%Y A379841 A002865 counts partitions into parts > 1, strict A025147.
%Y A379841 A318950 counts factorizations by sum.
%Y A379841 A379681 gives sum + product of prime indices.
%Y A379841 Cf. A069016, A319000, A319057, A319916, A325036, A326152, A379720, A379840.
%K A379841 nonn
%O A379841 1,2
%A A379841 _Gus Wiseman_, Jan 09 2025