
COMMENTS

No other elements below 10^10 (Ecker, 2002). Probably finite and complete.
For any n, there is the multiset {n, 2, 1^(n2)} with sum and product 2n.
(A) If n1 is composite (n1=ab), then {a+1, b+1, 1^(n2)} is another multiset with sum = product. (Hugo van der Sanden)
(B) If 2n1 is composite (2n1=ab), then {2, (a+1)/2, (b+1)/2, 1^(n3)} is another such multiset. (Don Reble)
(C) If n = 30k+12, then {2, 2, 2, 2, 2k+1, 1^(30k+7)} is another such multiset. (Don Reble)
Conditions (A), (B), (C) eliminate all n's except for 2, 3, 4, 6, 30k+0, and 30k+24.


REFERENCES

J.M. De Koninck, Ces nombres qui nous fascinent, Entry 174, p. 54, Ellipses, Paris 2008.
R. K. Guy, 'Unsolved Problems in Number Theory' (Section D24).
