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COMMENTS
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The multiset for n is {n, 2, 1x(n-2)} with sum and product 2n.
No other elements <= 3634884924 (Louis Marmet). Probably finite and complete.
A) If n-1 is composite (n-1=ab), then {a+1, b+1, 1x(n-2)} is another multiset with sum = product. (Hugo van der Sanden)
B) If 2n-1 is composite (2n-1=ab), then {2, (a+1)/2, (b+1)/2, 1x(n-3)} is another such multiset. (Don Reble)
C) If n = 30k+12, then {2, 2, 2, 2, 2k+1, 1x(30k+7)} is another such multiset. (Don Reble)
A,B,C eliminate all n's except for 2, 3, 4, 6, 30k+0 and 30k+24.
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REFERENCES
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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).
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