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 A341865 #16 Mar 23 2021 04:53:14
%S A341865 1,1,1,2,1,3,1,5,5,5,1,8,1,7,9,12,1,13,1,14,13,11,1,19,17,13,21,20,1,
%T A341865 23,1,27,21,17,25,30,1,19,25,33,1,33,1,32,37,23,1,42,37,41,33,38,1,47,
%U A341865 41,47,37,29,1,52,1,31,53,58
%N A341865 The cardinality of the largest multiset of positive integers whose product and sum equals n.
%C A341865 The largest multisets are given by the prime factorization of n and 1s added until the sum equals the product.
%F A341865 a(n) = n - Sum_(d_i*(p_i-1)), where n = Product_(p_i^d_i).
%F A341865 a(n) = n - A059975(n). - _Joerg Arndt_, Feb 22 2021
%e A341865 For n = 12, the set of size a(12) = 8 is {1,1,1,1,1,2,2,3}.
%o A341865 (PARI) a(n) = my(f=factor(n)); n - sum(k=1, #f~, f[k,2]*(f[k,1]-1)); \\ _Michel Marcus_, Feb 26 2021
%Y A341865 Cf. A059975, A104173, A033178, A033179, A341866.
%K A341865 nonn
%O A341865 1,4
%A A341865 _Nathaniel Gregg_, Feb 22 2021