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 A341866 #11 Mar 24 2021 03:05:06
%S A341866 1,1,1,2,1,3,1,4,5,5,1,6,1,7,9,8,1,9,1,10,13,11,1,12,17,13,17,14,1,15,
%T A341866 1,16,21,17,25,18,1,19,25,20,1,21,1,22,29,23,1,24,37,25,33,26,1,27,41,
%U A341866 28,37,29,1,30,1,31,41,32
%N A341866 The cardinality of the smallest (nontrivial, except for prime n) multiset of positive integers whose product and sum equal n.
%C A341866 The smallest set is obtained by taking the largest such multiset (A341865(n)) and replacing the largest proper subset that is also a product-sum multiset with its product. A singleton would always be the smallest product-sum multiset, so those are excluded except for prime n where no nontrivial multisets exist.
%F A341866 a(n) = (n/p - 1)*(p-1) + 1, where p is the smallest factor of n.
%F A341866 a(n) = A341865(n) - A341865(n/p) + 1, where p is the smallest prime factor of n.
%e A341866 For n = 12, the set of size a(n) = 6 is {1,1,1,1,2,6}.
%o A341866 (PARI) a(n) = if (n==1, 1, my(p=vecmin(factor(n)[,1])); (n/p-1)*(p-1) + 1); \\ _Michel Marcus_, Feb 26 2021
%Y A341866 Cf. A104173, A033178, A033179, A341865.
%Y A341866 Equals A330492 + 1. - _Hugo Pfoertner_, Feb 23 2021
%K A341866 nonn
%O A341866 1,4
%A A341866 _Nathaniel Gregg_, Feb 22 2021