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+load 'stats'
+
+NB. rank, combine, f, factorsof1, factorsof and helper are all helper functions used by factors
+NB. to find all factorizations of a number. Works but is not so nice :)
+
+rank=:{.@$@$
+combine=: (*./`])@.(1: = rank)
+
+f=: dyad define
+factors=.x
+length=.$factors
+keep=.y{factors
+rest=.(combine y~:"0 _ i.length)#factors
+(*/rest),keep
+)
+
+factorsof1=: monad define
+len=.$y
+((y&f)"1)@comb&len len-2
+)
+
+factorsof=: monad define
+cols=.<:{:$y
+vals=.;factorsof1"1 y
+rows=.($vals) % cols
+~. (rows,cols)$vals
+)
+
+helper=: dyad : '<"1 factorsof^:x (1,$y)$y'
+
+factors=: monad define
+pfacts=.q:y
+;(helper&pfacts) each i.$pfacts
+)
+
+NB. runme creates a large list of every possible factorization of numbers from 2 to 2*k
+NB. Then it goes over that list and updates the numbers array with the smallest
+NB. product-sum number. product-sum numbers from a set of factors such as 3 2 2 by adding
+NB. enough ones, since that makes the sum large enough. the k for which a set of factors
+NB. can be used can be calculated by (prod-sum)+$factors
+NB. and can be read as "number of ones needed" + "number of factors"
+NB. The slowest part of the program is finding all factorizations of numbers.
+
+runme=: monad define
+maxk=.y
+maxn=.2*maxk
+facts=. ; factors each 2+i.(maxn-1)
+numbers=. maxn$_
+factorcount=.$facts
+index=.0
+while. index < factorcount do.
+	nums=.>index{facts
+	index=. >:index
+	sum=.+/nums
+	prod=.*/nums
+	n=.(prod-sum)+$nums NB. any factors can be used when padded with enough ones :)
+	oldprod=.n{numbers
+	if. prod < oldprod do.
+		numbers=.prod n} numbers
+	end.
+end.
+numbers=. (-maxk-1)}. 2}. numbers NB. drop for k=0,1, and take (maxk-1) elements
++/~.numbers
+)
+\ No newline at end of file