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%I #11 Jun 07 2012 00:51:48
%S 1,3,12,10,19,26,33,39,55,74,48,62,71,99,45,140,96,176,104,144,159,
%T 175,230,191,320,328,240,334,259,344,279,308,303,505,419,560,714,550,
%U 455,665,684,670,751,935,899,800,1051,776,928,602,749,1104,689,1295,1364
%N Smallest number m such that there are exactly n ways to partition the numbers {1,...,m} into nonempty sets P and S with the product of the elements of P equal to the sum of elements in S.
%C A178830(a(n)) = n and A178830(m) <> n for m < a(n).
%e a(1) = 3: 3 = 1+2;
%e a(2) = 12: 1*5*12 = 2+3+4+6+7+8+9+10+11, 2*4*8 = 1+3+5+6+7+9+10+11+12;
%e a(3) = 10: 1*2*3*7 = 4+5+6+8+9+10, 1*4*10 = 2+3+5+6+7+8+9, 6*7 = 1+2+3+4+5+8+9+10.
%o (Haskell)
%o import Data.List (elemIndex)
%o import Data.Maybe (fromJust)
%o a207852 n = (fromJust $ elemIndex n a178830_list) + 1
%K nonn
%O 0,2
%A _Reinhard Zumkeller_, Feb 21 2012
%E a(25)-a(54) from _Alois P. Heinz_, Jun 07 2012
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