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

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, 30375000, 1, 2, 3, 4, 5, 6, 7, 750453558750000, 1, 2, 3, 4, 5, 6, 7, 8, 19699405917187500, 1, 2, 3, 4, 5, 6, 7, 8, 9, 459652804734375000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9652708899421875000

Offset: 1

Author

Amarnath Murthy, Mar 20 2003

Keywords

• nonn
• tabl

Comments

The n-th row has the form {1,2,...,n-1,x}, where x is as small as possible.

Examples

			Triangle begins:
  1;
  1, 4;
  1, 2, 4;
  1, 2, 3, 216;
  1, 2, 3,   4, 324;
  1, 2, 3,   4,   5, 6075000;
  ...
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1485 (rows 1 to 54, flattened)

Crossrefs

Cf. A080509, A080510, A080504, A080511.

Programs

Maple

f:= proc(n) local F;
  F:= ifactors((n-1)!)[2];
  mul(t[1]^(n-(t[2] mod n)),t=F)
end proc:
f(2):= 4:
seq(op([seq(j,j=1..i-1),f(i)]),i=1..20); # Robert Israel, Nov 04 2018

Mathematica

MapAt[{First@ #, 4 Last@ #} &, Array[Append[Range[# - 1], Apply[Times, Prime@ Range@ PrimePi[# - 1]]^#/(# - 1)!] &, 11], 2] // Flatten (* Michael De Vlieger, Nov 05 2018 *)

Extensions

More terms using A080509 from Michel Marcus, Nov 04 2018