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%I #15 Aug 22 2024 09:17:40
%S 1,15,207,2544,30091,347096,3931343,43906441,484912312,5306957044
%N Integer part of the geometric mean of all the distinct numbers formed by permuting the digits of concatenation of numbers from 1 to n.
%C For n < 10 there are n! distinct numbers.
%e a(3) = floor((123*132*213*231*312*321)^(1/6)) = floor(207.581...) = 207.
%e a(4) = floor((1234*1243*1324*1342*1423*1432*...*4312*4321)^(1/24)) = floor(2544.967...) = 2544.
%t a[n_] := Floor[ (Times @@ FromDigits /@ Permutations[Range[n]])^(1/n!) ]; Table[a[n], {n, 1, 10}] (* _Ryan Propper_, Jul 21 2006 *)
%Y Cf. A071268, A078266.
%K base,more,nonn
%O 1,2
%A _Amarnath Murthy_, Nov 24 2002
%E More terms from _Ryan Propper_, Jul 21 2006