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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