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

0,2

Links

Table of n, a(n) for n=0..12.

Christian Krause, Jamie Morken, et al., A mined LODA assembly source for this sequence

Don Reble, Python program

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)

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A168510 A324235 A125531 * A107101 A147780 A361524

Adjacent sequences: A095206 A095207 A095208 * A095210 A095211 A095212

Keyword

nonn

Author

Amarnath Murthy, Jun 08 2004

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

Status

approved