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 A033178 #26 Nov 13 2024 22:33:04
%S A033178 1,1,1,3,1,2,2,2,2,3,2,4,2,2,2,4,2,4,2,4,2,4,1,5,4,3,3,5,2,4,3,5,2,3,
%T A033178 2,6,3,3,4,7,2,5,2,4,4,5,2,5,4,4,3,7,2,5,4,5,4,4,2,9,3,4,4,7,2,5,5,4,
%U A033178 3,6,3,9,4,3,3,6,3,5,2,7,4,5,2,10,5,4,5,8,2,6,3,6,3,6,5,6,5,4,5,8,3,6,3,5
%N A033178 Number of multisets of n positive integers with equal sum and product.
%C A033178 The multiset {n^1, 2^1, 1^(n-2)} has n elements and sum = product = 2n. Hence a(n) >= 1.
%D A033178 R. K. Guy, 'Unsolved Problems in Number Theory' (Section D24).
%H A033178 David Radcliffe, <a href="/A033178/b033178.txt">Table of n, a(n) for n = 2..10000</a>
%H A033178 Onno M. Cain, <a href="https://arxiv.org/abs/1908.03235">Bioperational Multisets in Various Semi-rings</a>, arXiv:1908.03235 [math.RA], 2019.
%H A033178 L. Kurlandchik and A. Nowicki, <a href="https://doi.org/10.2307/3621488">When the sum equals the product</a>, The Mathematical Gazette, 84(499) (2000), 91-94. doi:10.2307/3621488.
%H A033178 Burkard Polster, <a href="https://www.youtube.com/watch?v=phqXU-1CFas">What's the next freak identity? A new deep connection with Sophie Germain primes</a>, YouTube Mathologer video, 2024.
%e A033178 a(5) = 3: {2,2,2,1,1}, {3,3,1,1,1}, {5,2,1,1,1}.
%e A033178 a(7) = 2: {4,3,1,1,1,1,1}, {7,2,1,1,1,1,1}.
%Y A033178 Cf. A033179, A104173.
%K A033178 nonn
%O A033178 2,4
%A A033178 _David W. Wilson_