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

1, 4, 6, 8, 10, 11, 12, 14, 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, 78

Offset: 1

Author

Gus Wiseman, Jan 09 2025

Keywords

• nonn

Examples

			For sum + product = 14 we have two possibilities: {7} or {2,4}; so 14 is in the sequence.
		

Crossrefs

The version allowing 1's is A326178.

Positions of nonzeros in A379679.

The complement is A379680.

The non-strict version is A379839, complement A379670.

For unique (instead of some) we have A379842.

Arrays counting multisets by sum and product: A379666, A379671, A379678.

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.

A379681 gives sum + product of prime indices.

Cf. A069016, A319000, A319057, A319916, A325036, A326152, A379720, A379840.

Programs

Mathematica

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