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%I #12 Aug 23 2012 21:04:55
%S 0,0,1,0,0,1,0,0,3,25,0,0,0,2,7,0,0,0,0,68,623,0,0,0,0,0,124,1183,0,0,
%T 0,0,0,0,2338,24603,0,0,0,0,0,0,3,598,5895,0,0,0,0,0,0,0,0,161947,
%U 2017603
%N Triangle T(b,k) read by rows, giving numbers of pairs of unequal permutations of all the digits 1, ..., k in base b (k<b) whose ratio is an integer.
%C Terms computed by Michael Trott.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SteffiProblem.html">Steffi Problem</a>
%e Triangle is arranged as (b,k) = (3, 2), (4, 2), (4, 3), (5, 2), (5, 3), (5,4), (6,2), ....
%e In base 3, there are no solutions for 12, so T(3,2)=0. In base 4, there are no solutions for 12, so T(4,2)=0 and a single solution for 123, so T(4,3)=1. In base 5, there are no solutions with the digits 12 or 123, so T(5,1)=T(5,2)=0, but there is a single solution with the digits 1234: 4312_5/1234_5 = 3, so T(5,3)=1.
%e 0;
%e 0, 1;
%e 0, 0, 1;
%e 0, 0, 3, 25;
%e 0, 0, 0, 2, 7;
%e 0, 0, 0, 0, 68, 623;
%e 0, 0, 0, 0, 0, 124, 1183;
%Y T(b,b-1) gives A080203.
%K nonn,tabl,base
%O 3,9
%A _Eric W. Weisstein_, Feb 05 2003
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