A080509 -id:A080509 - 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.

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

Amarnath Murthy, Mar 20 2003

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

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

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

Cf. A080509, A080510, A080504, A080511.

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

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

More terms using A080509 from Michel Marcus, Nov 04 2018

A186944 Geometric mean of n-th row of A080508.

Original entry on oeis.org

1, 2, 2, 6, 6, 30, 30, 210, 210, 210, 210, 2310, 2310, 30030, 30030, 30030, 30030, 510510, 510510, 9699690, 9699690, 9699690, 9699690, 223092870, 223092870, 223092870, 223092870, 223092870, 223092870, 6469693230, 6469693230, 200560490130, 200560490130

Offset: 1

Michel Marcus, Aug 30 2013

nonn

Cf. A080509, A083907, A034386.

a(n) = {if (n == 1, return (1)); if (n == 2, return (2)); f  = factor((n-1)!); prod(i=1, #f~, f[i,1]);} \\ Michel Marcus, Aug 30 2013

a(n) = if(n==2, 2, prod(i=1,primepi(n-1),prime(i))) \\ Jeppe Stig Nielsen, Nov 04 2018

For n != 2, a(n) = A034386(n-1). - Jeppe Stig Nielsen, Nov 04 2018

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.

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