OFFSET
1,6
COMMENTS
a(n-1) <= a(n) <= n^2.
LINKS
Steve Butler, Table of n, a(n) for n = 1..500
EXAMPLE
For n=6 we have a(n)=4; 1 is impossible because 1*6=2*3, 2 is impossible because 2*6=3*4, and 3 is impossible because 3*8=4*6; however, the products of pairs of distinct numbers from {4,5,6,7,8,9}, i.e., 20,24,28,30,32,35,36,40,42,45,48,54,56,63,72, are all distinct. (Note that we do not count 6*6=4*9 since 6*6 does not involve distinct terms.)
MATHEMATICA
a[1]=1; a[n_] := a[n] = Block[{k = a[n-1]}, While[Min@ Differences@ Sort[Times @@@ Subsets[Range[k, n+k-1], {2}]] == 0, k++]; k]; Array[a, 60] (* Giovanni Resta, Mar 14 2014 *)
PROG
(Sage)
def find_start(n):
q=1
while True:
L={}
advance=True
for i in range(n-1):
for j in range(i+1, n):
if (q+i)*(q+j) not in L:
L[(q+i)*(q+j)]=1
else:
advance=False
break
if not advance:
break
else:
return q
q+=1
CROSSREFS
KEYWORD
nonn
AUTHOR
Steve Butler, Mar 13 2014
STATUS
approved