A095209 a(0) = 1, and for n > 0, a(n) = the least multiple of prime(n) such that the geometric mean of a(0) to a(n) is an integer.

1, 4, 54, 3750, 504210, 372027810, 144949074270, 209481995953230, 164735296593157290, 401824316553919068810, 2721846739094340967339230, 5095936579799734140259818030, 48850362989361131638352534231610

Offset: 0

Author

Amarnath Murthy, Jun 08 2004

Keywords

• nonn

Examples

			(1*4*54*3750)^(1/4) = 30.
		

Links

• Christian Krause, Jamie Morken, et al., A mined LODA assembly source for this sequence
• Don Reble, Python program

Crossrefs

Cf. A000040, A002110, A020522, A057335, A095210, A307539.

Programs

Mathematica

{1}~Join~MapIndexed[Prime[First[#2]]^First[#2]*#1 &, FoldList[Times, Prime@ Range[12]]] (* Michael De Vlieger, Jul 01 2022 *)

PARI

A002110(n)=prod(i=1, n, prime(i));
A095209(n) = if(0==n, 1, prime(n)^(n)*A002110(n)); \\ Antti Karttunen, Jun 28 2022

Formula

From Antti Karttunen and Peter Munn, May 04 2022: (Start)

The n-th partial product of these terms = A002110(n)^(1+n), i.e., the n-th geometric mean is the n-th power of (n-1)-th primorial.

a(n) = A002110(n) * A307539(n).

a(n) = A057335(A020522(n)). [Found by LODA-miner, follows from the above formulas]

(End)

Extensions

Edited by Don Reble, Jan 06 2007

Starting offset changed from 1 to 0 and the definition accordingly edited by Antti Karttunen, May 04 2022