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A362364 a(n) is the product of the first n primes that are coprime to a(n-1); a(0) = 1.

%I A362364 #37 Apr 23 2023 22:41:31
%S A362364 1,2,15,154,3315,67298,2980185,102091066,6022953885,319238763382,
%T A362364 24615812527995,1654614510608906,161405882746063215,
%U A362364 14284287070086685498,1679105398207295625645,166597640098421012963174,24096841569672899523631395,2989927846846361919650083778,499069685749495422033929821845
%N A362364 a(n) is the product of the first n primes that are coprime to a(n-1); a(0) = 1.
%C A362364 Lexicographically first sequence of squarefree numbers such that A001222(a(n)) = n and each term is coprime to the next.
%H A362364 Robert Israel, <a href="/A362364/b362364.txt">Table of n, a(n) for n = 0..315</a>
%F A362364 If n is even, a(n) = Product_{i=1..n/2} prime(4*i-2)*prime(4*i-1).
%F A362364 If n is odd, a(n) = 2 * Product_{i=1..(n-1)/2} prime(4*i)*prime(4*i+1).
%F A362364 From _Peter Munn_, Apr 21 2023: (Start)
%F A362364 a(0) = 1, for n >= 1, a(n) = A002110(2n-1)/a(n-1).
%F A362364 a(n) = A019565(A037481(n)).
%F A362364 For n >= 1, a(n-1) = A117214(A100112(a(n))).
%F A362364 (End)
%e A362364 a(0) = 1.
%e A362364 a(1) = 2 is the least prime coprime to a(0).
%e A362364 a(2) = 3*5 is the product of the two least primes coprime to a(1).
%e A362364 a(3) = 2*7*11 is the product of the three least primes coprime to a(2).
%e A362364 a(4) = 3*5*13*17 = 3315 is the product of the four least primes coprime to a(3).
%p A362364 f:= proc(n) local i;
%p A362364    if n::odd then 2 * mul(ithprime(4*i)*ithprime(4*i+1),i=1..(n-1)/2)
%p A362364    else mul(ithprime(4*i-2)*ithprime(4*i-1),i=1..(n/2))
%p A362364    fi
%p A362364 end proc:
%p A362364 map(f, [$0..20]);
%o A362364 (Python)
%o A362364 from math import prod
%o A362364 from sympy import prime
%o A362364 def A362364(n): return prod(prime(i)*prime(i+1) for i in range(2+((n&1)<<1),(n<<1)-1,4))<<(n&1) # _Chai Wah Wu_, Apr 20 2023
%Y A362364 Cf. A001222.
%Y A362364 See the formula section for the relationships with A002110, A019565, A037481, A100112, A117214.
%K A362364 nonn
%O A362364 0,2
%A A362364 _Robert Israel_, Apr 18 2023