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%I #21 Jul 30 2015 01:42:30
%S 0,0,1,1,25,7,623,1183,24603,5895,2017603,242283
%N Steffi sequence; the numbers of pairs of unequal permutations of all the digits 1, ..., b-1 in base 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 In base 2, there are no solutions for 1, so a(2)=0. In base 3, there are no solutions for 12, so a(3)=0. In base 4, there is a single solutions for 123, so a(4)=1. In base 5, there is a single solution with the digits 1234: 4312_5/1234_5 = 3, so a(5)=1.
%t f[n_] := Block[{p = FromDigits[ #, n] & /@ Permutations[ Range[n - 1]]}, Sum[ Length[ Select[ p/p[[i]], IntegerQ[ # ] &]], {i, (n - 1)!}] - (n - 1)! ]; Table[ f[n], {n, 2, 9}] (* _Robert G. Wilson v_, Jul 15 2005 *)
%Y T(b-1, b) entries of A080202.
%K nonn,hard,base,more
%O 2,5
%A _Eric W. Weisstein_, Feb 05 2003
%E Prepended a(2)=0, added a(13) - _Giovanni Resta_, Feb 24 2013