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

1,3

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A080509, A080510, A080504, A080511.

Sequence in context: A072033 A100353 A366397 * A178141 A063987 A236269

Adjacent sequences: A080505 A080506 A080507 * A080509 A080510 A080511

Keyword

nonn,tabl

Author

Amarnath Murthy, Mar 20 2003

Extensions

More terms using A080509 from Michel Marcus, Nov 04 2018

Status

approved