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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.

%I A095209 #33 Jul 03 2022 09:20:40
%S A095209 1,4,54,3750,504210,372027810,144949074270,209481995953230,
%T A095209 164735296593157290,401824316553919068810,2721846739094340967339230,
%U A095209 5095936579799734140259818030,48850362989361131638352534231610
%N 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.
%H A095209 Christian Krause, Jamie Morken, et al., <a href="https://github.com/loda-lang/loda-programs/blob/main/oeis/095/A095209.asm">A mined LODA assembly source for this sequence</a>
%H A095209 Don Reble, <a href="/A095209/a095209.py.txt">Python program</a>
%F A095209 From _Antti Karttunen_ and _Peter Munn_, May 04 2022: (Start)
%F A095209 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.
%F A095209 a(n) = A002110(n) * A307539(n).
%F A095209 a(n) = A057335(A020522(n)). [Found by LODA-miner, follows from the above formulas]
%F A095209 (End)
%e A095209 (1*4*54*3750)^(1/4) = 30.
%t A095209 {1}~Join~MapIndexed[Prime[First[#2]]^First[#2]*#1 &, FoldList[Times, Prime@ Range[12]]] (* _Michael De Vlieger_, Jul 01 2022 *)
%o A095209 (PARI)
%o A095209 A002110(n)=prod(i=1, n, prime(i));
%o A095209 A095209(n) = if(0==n, 1, prime(n)^(n)*A002110(n)); \\ _Antti Karttunen_, Jun 28 2022
%Y A095209 Cf. A000040, A002110, A020522, A057335, A095210, A307539.
%K A095209 nonn
%O A095209 0,2
%A A095209 _Amarnath Murthy_, Jun 08 2004
%E A095209 Edited by _Don Reble_, Jan 06 2007
%E A095209 Starting offset changed from 1 to 0 and the definition accordingly edited by _Antti Karttunen_, May 04 2022