A033178 - OEIS

%I #20 Jul 03 2020 18:33:51

%S 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 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 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 Number of multisets of n positive integers with equal sum and product.

%C The multiset {n^1, 2^1, 1^(n-2)} has n elements and sum = product = 2n. Hence a(n) >= 1.

%D R. K. Guy, 'Unsolved Problems in Number Theory' (Section D24).

%H David Radcliffe, <a href="/A033178/b033178.txt">Table of n, a(n) for n = 2..10000</a>

%H 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 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.

%Y Cf. A033179, A104173.

%K nonn

%O 2,4

%A _David W. Wilson_