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

1, 4, 6, 8, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

Author

Gus Wiseman, Jan 04 2025

Keywords

• nonn

Comments

A superset of A379840.

Examples

			We have {2,5} with sum + product = 17, so 17 is in the sequence.
We have {2,3,5,5} with sum + product = 165, so 165 is in the sequence.
		

Crossrefs

The complement is A379670.

The strict version is A379841, see A379842.

Arrays counting multisets by sum and product:

- partitions: A379666, antidiagonal sums A379667

- partitions without ones: A379668, antidiagonal sums A379669

- strict partitions: A379671, antidiagonal sums A379672

- strict partitions without ones: A379678, antidiagonal sums A379679

Counting and ranking multisets by comparing sum and product:

- same: A001055 (strict A045778), ranks A301987

- divisible: A057567, ranks A326155

- divisor: A057568, ranks A326149, see A326156, A326172, A379733

- greater: A096276 shifted right, ranks A325038

- greater or equal: A096276, ranks A325044

- less: A114324, ranks A325037, see A318029

- less or equal: A319005, ranks A379721

- different: A379736, ranks A379722, see A111133

A002865 counts partitions into parts > 1, strict A025147.

A318950 counts factorizations by sum.

Cf. A003963, A069016, A319000, A319057, A319916, A325036, A326152, A326178, A379680, A379720, A379840.

Programs

Mathematica

nn=100;
facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
Intersection[Range[nn],Total[#]+Times@@#&/@Join@@Array[facs,nn]]