cp's OEIS Frontend

A379840 Numbers that are the sum + product of a unique multiset of positive integers > 1.

%I A379840 #9 Jan 12 2025 10:15:17
%S A379840 1,4,6,10,11,12,15,16,17,18,22,27,28,30,31,43,52,58,61,67,70,73,91,97,
%T A379840 100,102,108,115,130,145,147,148,162,165,171,217,262,277,283,291,361,
%U A379840 430,481,508,577,633,652,682,763,1093,1137,1201,1513,1705,2257,2401,2653,3133,4123,5113,5905
%N A379840 Numbers that are the sum + product of a unique multiset of positive integers > 1.
%e A379840 The only multiset with no 1's and sum + product = 165 is {2,3,5,5}, so 165 is in the sequence.
%t A379840 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&, Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A379840 Join@@Position[Table[Length[Select[Join@@Array[facs,n], Total[#]+Times@@#==n&]],{n,100}],1]
%Y A379840 Positions of 1 in A379669 (zeros A379670).
%Y A379840 For sets instead of multisets we have A379842, see A379841.
%Y A379840 Arrays counting multisets by sum and product:
%Y A379840 - partitions: A379666, antidiagonal sums A379667
%Y A379840 - partitions without ones: A379668, antidiagonal sums A379669
%Y A379840 - strict partitions: A379671, antidiagonal sums A379672
%Y A379840 - strict partitions without ones: A379678, antidiagonal sums A379679
%Y A379840 Counting and ranking multisets by comparing sum and product:
%Y A379840 - same: A001055 (strict A045778), ranks A301987
%Y A379840 - divisible: A057567, ranks A326155
%Y A379840 - divisor: A057568, ranks A326149, see A326156, A326172, A379733
%Y A379840 - greater: A096276 shifted right, ranks A325038
%Y A379840 - greater or equal: A096276, ranks A325044
%Y A379840 - less: A114324, ranks A325037, see A318029
%Y A379840 - less or equal: A319005, ranks A379721
%Y A379840 - different: A379736, ranks A379722, see A111133
%Y A379840 A002865 counts partitions into parts > 1, strict A025147.
%Y A379840 A318950 counts factorizations by sum.
%Y A379840 Cf. A003963, A069016, A319000, A319057, A319916, A325036, A326152, A379680.
%K A379840 nonn
%O A379840 1,2
%A A379840 _Gus Wiseman_, Jan 08 2025
%E A379840 More terms from _Jinyuan Wang_, Jan 12 2025