cp's OEIS Frontend

A379680 Numbers that are not the sum + product of any set of positive integers > 1. Zeros of A379679.

%I A379680 #9 Jan 06 2025 09:00:28
%S A379680 2,3,5,7,9,13,15,21,25,37,45,57,81,93,121,133,157,165,193,217,225,253,
%T A379680 273,297,325,477,525,613,981,1201,1213,1317,1813,1821,2401,4273,5113,
%U A379680 5905,7477
%N A379680 Numbers that are not the sum + product of any set of positive integers > 1. Zeros of A379679.
%C A379680 Is this sequence infinite?
%C A379680 Are all terms odd except for 2?
%e A379680 The set {2,3,4} has sum + product equal to 9 + 24 = 33, so 33 is not in the sequence.
%t A379680 nn=1000;
%t A379680 strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A379680 Complement[Range[nn],Total[#]+Times@@#&/@Join@@Array[strfacs,nn]]
%Y A379680 The non-strict version is A379670.
%Y A379680 The complement is A379841, a superset of A379842.
%Y A379680 Arrays counting multisets by sum and product:
%Y A379680 - partitions: A379666, antidiagonal sums A379667
%Y A379680 - partitions without ones: A379668, antidiagonal sums A379669
%Y A379680 - strict partitions: A379671, antidiagonal sums A379672
%Y A379680 - strict partitions without ones: A379678, antidiagonal sums A379679
%Y A379680 Counting and ranking multisets by comparing sum and product:
%Y A379680 - same: A001055 (strict A045778), ranks A301987
%Y A379680 - divisible: A057567, ranks A326155
%Y A379680 - divisor: A057568, ranks A326149, see A326156, A326172, A379733
%Y A379680 - greater: A096276 shifted right, ranks A325038
%Y A379680 - greater or equal: A096276, ranks A325044
%Y A379680 - less: A114324, ranks A325037, see A318029
%Y A379680 - less or equal: A319005, ranks A379721
%Y A379680 - different: A379736, ranks A379722, see A111133
%Y A379680 A000041 counts integer partitions, strict A000009.
%Y A379680 A002865 counts partitions into parts > 1, strict A025147.
%Y A379680 A318950 counts factorizations by sum.
%Y A379680 A326622 counts factorizations with integer mean, strict A328966.
%Y A379680 Cf. A003963, A069016, A319000, A319057, A325036, A326178, A379720.
%K A379680 nonn,look,more
%O A379680 1,1
%A A379680 _Gus Wiseman_, Jan 04 2025