cp's OEIS Frontend

A379839 Numbers that are the sum + product of some multiset of positive integers > 1. Nonzeros of A379669.

%I A379839 #8 Jan 05 2025 22:36:18
%S A379839 1,4,6,8,10,11,12,14,15,16,17,18,19,20,22,23,24,26,27,28,29,30,31,32,
%T A379839 33,34,35,36,38,39,40,41,42,43,44,46,47,48,49,50,51,52,53,54,55,56,58,
%U A379839 59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77
%N A379839 Numbers that are the sum + product of some multiset of positive integers > 1. Nonzeros of A379669.
%C A379839 A superset of A379840.
%e A379839 We have {2,5} with sum + product = 17, so 17 is in the sequence.
%e A379839 We have {2,3,5,5} with sum + product = 165, so 165 is in the sequence.
%t A379839 nn=100;
%t A379839 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A379839 Intersection[Range[nn],Total[#]+Times@@#&/@Join@@Array[facs,nn]]
%Y A379839 The complement is A379670.
%Y A379839 The strict version is A379841, see A379842.
%Y A379839 Arrays counting multisets by sum and product:
%Y A379839 - partitions: A379666, antidiagonal sums A379667
%Y A379839 - partitions without ones: A379668, antidiagonal sums A379669
%Y A379839 - strict partitions: A379671, antidiagonal sums A379672
%Y A379839 - strict partitions without ones: A379678, antidiagonal sums A379679
%Y A379839 Counting and ranking multisets by comparing sum and product:
%Y A379839 - same: A001055 (strict A045778), ranks A301987
%Y A379839 - divisible: A057567, ranks A326155
%Y A379839 - divisor: A057568, ranks A326149, see A326156, A326172, A379733
%Y A379839 - greater: A096276 shifted right, ranks A325038
%Y A379839 - greater or equal: A096276, ranks A325044
%Y A379839 - less: A114324, ranks A325037, see A318029
%Y A379839 - less or equal: A319005, ranks A379721
%Y A379839 - different: A379736, ranks A379722, see A111133
%Y A379839 A002865 counts partitions into parts > 1, strict A025147.
%Y A379839 A318950 counts factorizations by sum.
%Y A379839 Cf. A003963, A069016, A319000, A319057, A319916, A325036, A326152, A326178, A379680, A379720, A379840.
%K A379839 nonn
%O A379839 1,2
%A A379839 _Gus Wiseman_, Jan 04 2025