cp's OEIS Frontend

A080508 Triangle whose n-th row contains the least set (ordered lexicographically) of n distinct positive integers whose geometric mean is an integer.

%I A080508 #13 Nov 05 2018 21:01:35
%S A080508 1,1,4,1,2,4,1,2,3,216,1,2,3,4,324,1,2,3,4,5,6075000,1,2,3,4,5,6,
%T A080508 30375000,1,2,3,4,5,6,7,750453558750000,1,2,3,4,5,6,7,8,
%U A080508 19699405917187500,1,2,3,4,5,6,7,8,9,459652804734375000,1,2,3,4,5,6,7,8,9,10,9652708899421875000
%N A080508 Triangle whose n-th row contains the least set (ordered lexicographically) of n distinct positive integers whose geometric mean is an integer.
%C A080508 The n-th row has the form {1,2,...,n-1,x}, where x is as small as possible.
%H A080508 Robert Israel, <a href="/A080508/b080508.txt">Table of n, a(n) for n = 1..1485</a> (rows 1 to 54, flattened)
%e A080508 Triangle begins:
%e A080508   1;
%e A080508   1, 4;
%e A080508   1, 2, 4;
%e A080508   1, 2, 3, 216;
%e A080508   1, 2, 3,   4, 324;
%e A080508   1, 2, 3,   4,   5, 6075000;
%e A080508   ...
%p A080508 f:= proc(n) local F;
%p A080508   F:= ifactors((n-1)!)[2];
%p A080508   mul(t[1]^(n-(t[2] mod n)),t=F)
%p A080508 end proc:
%p A080508 f(2):= 4:
%p A080508 seq(op([seq(j,j=1..i-1),f(i)]),i=1..20); # _Robert Israel_, Nov 04 2018
%t A080508 MapAt[{First@ #, 4 Last@ #} &, Array[Append[Range[# - 1], Apply[Times, Prime@ Range@ PrimePi[# - 1]]^#/(# - 1)!] &, 11], 2] // Flatten (* _Michael De Vlieger_, Nov 05 2018 *)
%Y A080508 Cf. A080509, A080510, A080504, A080511.
%K A080508 nonn,tabl
%O A080508 1,3
%A A080508 _Amarnath Murthy_, Mar 20 2003
%E A080508 More terms using A080509 from _Michel Marcus_, Nov 04 2018