cp's OEIS Frontend

A379670 Numbers that are not the sum + product of any multiset of positive integers > 1. Zeros of A379669.

%I A379670 #9 Jan 05 2025 22:36:29
%S A379670 2,3,5,7,9,13,21,25,37,45,57,81,133,157,193,225,253,273,325,477,613,
%T A379670 1821
%N A379670 Numbers that are not the sum + product of any multiset of positive integers > 1. Zeros of A379669.
%C A379670 Is this sequence infinite?
%C A379670 Are all terms odd except for 2?
%e A379670 The partition (3,2,2) has sum + product equal to 7 + 12 = 19, so 19 is not in the sequence.
%t A379670 nn=1000;
%t A379670 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A379670 Complement[Range[nn],Total[#]+Times@@#&/@Join@@Array[facs,nn]]
%Y A379670 The strict case is A379680.
%Y A379670 The complement is A379839, a superset of A379840.
%Y A379670 Arrays counting multisets by sum and product:
%Y A379670 - partitions: A379666, antidiagonal sums A379667
%Y A379670 - partitions without ones: A379668, antidiagonal sums A379669
%Y A379670 - strict partitions: A379671, antidiagonal sums A379672
%Y A379670 - strict partitions without ones: A379678, antidiagonal sums A379679
%Y A379670 Counting and ranking multisets by comparing sum and product:
%Y A379670 - same: A001055 (strict A045778), ranks A301987
%Y A379670 - divisible: A057567, ranks A326155
%Y A379670 - divisor: A057568, ranks A326149, see A326156, A326172, A379733
%Y A379670 - greater: A096276 shifted right, ranks A325038
%Y A379670 - greater or equal: A096276, ranks A325044
%Y A379670 - less: A114324, ranks A325037, see A318029
%Y A379670 - less or equal: A319005, ranks A379721
%Y A379670 - different: A379736, ranks A379722, see A111133
%Y A379670 A000041 counts integer partitions, strict A000009.
%Y A379670 A002865 counts partitions into parts > 1, strict A025147.
%Y A379670 A318950 counts factorizations by sum.
%Y A379670 Cf. A003963, A069016, A319000, A319057, A325036, A326152, A379720.
%K A379670 nonn,more
%O A379670 1,1
%A A379670 _Gus Wiseman_, Jan 04 2025