This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A343297 #17 Jul 11 2021 10:23:15
%S A343297 7,8,9,10,12,14,15,16,18,20,22,30,34,36,42,44,48,54,60,66,80,84,90,
%T A343297 112,126,142,192,210,234,252,258,330,350,354,440,594,654,714,720,780,
%U A343297 966,1102,2400,2820,4350,4354,5274,6174,6324
%N A343297 Numbers k such that there are exactly two multisets of cardinality k where the sum equals the product (A033178(k)=2).
%C A343297 At most one of a(n) - 1 and 2*a(n)-1 are composite. More precisely, a(n) are those positive integers such that exactly one of product(s)*(a(n)+sum(s)-k-2)+1 can be factored as (product(s)*p-1)*(product(s)*q-1), where s varies over all multisets of k positive integers and 1 < p <= q < a(n). The first statement is given by considering s = {} and s = {2}. a(50) is greater than 10^4.
%H A343297 Michael W. Ecker, <a href="https://www.jstor.org/stable/3219187?seq=1">When Does a Sum of Positive Integers Equal Their Product?</a>, Mathematics Magazine 75(1), 2002, pp. 41-47.
%e A343297 a(5) = 12 because {2,2,2,2,1,1,1,1,1,1,1,1} and {12,2,1,1,1,1,1,1,1,1,1,1} are the only multisets of size 12 where the sum equals the product.
%Y A343297 Cf. A033178, A033179, A343298.
%K A343297 nonn
%O A343297 1,1
%A A343297 _Nathaniel Gregg_, Apr 11 2021