Proposes updates to A033178, A033179.

David Wilson davidwwilson at comcast.net
Thu Apr 7 23:43:22 CEST 2005


%I A033178
%N A033178 Number of multisets of n positive integers with equal sum and 
product.
%C A033178 The multiset {n, 2, 1x(n-2)} has n elements and sum = product = 
2n.  Hence a(n) >= 1.

%I A033179
%N A033179 Exactly one multiset of n positive integers has equal sum and 
product.
%C A033179 The multiset for n is {n, 2, 1x(n-2)} with sum and product 2n.
%C A033179 No other elements <= 3634884924 (Louis Marmet).  Probably finite 
and complete.
%C A033179 If n = composite+1 = ab+1 (a,b >= 2), then {ab+1, 2, 1x(ab-1)} 
and (a+1, b+1, 1x(ab-1)} are distinct n-element multisets with sum = 
product, and n is not in this sequence.  Hence all n > 2 in this sequence 
are of the form prime+1 (Hugo van der Sanden).

- David W. Wilson

"Truth is just truth -- You can't have opinions about the truth."
   - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings" 






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