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A080203 Steffi sequence; the numbers of pairs of unequal permutations of all the digits 1, ..., b-1 in base b whose ratio is an integer. 1

%I

%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

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)