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A371099 a(n) = gcd(36*n+9, A276086(36*n+9)), where A276086 is the primorial base exp-function.

%I A371099 #11 Mar 10 2024 19:54:49
%S A371099 3,15,3,3,3,21,75,3,33,3,3,15,3,3,3,3,15,3,3,231,3,15,3,3,3,3,105,3,3,
%T A371099 3,363,75,3,21,3,3,15,3,3,3,21,165,3,3,3,3,15,3,3,3,3,15,33,3,21,3,75,
%U A371099 3,3,3,3,735,3,33,3,3,15,3,273,3,3,15,3,3,33,21,15,3,3,3,3,975,3,3,3,33,15,3,3,21,3,15
%N A371099 a(n) = gcd(36*n+9, A276086(36*n+9)), where A276086 is the primorial base exp-function.
%C A371099 All terms are multiples of 3, with A007949(a(n)) = 1 for all n.
%H A371099 Antti Karttunen, <a href="/A371099/b371099.txt">Table of n, a(n) for n = 0..11550</a>
%H A371099 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A371099 a(n) = A324198(A139609(n)).
%t A371099 f[x_] := Block[{m, i, n = x, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; m]; Array[GCD[#, f[#]] &[36 # + 9] &, 100, 0] (* _Michael De Vlieger_, Mar 10 2024, after _Jean-François Alcover_ at A276086 *)
%o A371099 (PARI)
%o A371099 A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
%o A371099 A371099(n) = A324198((36*n)+9);
%Y A371099 Cf. A007949, A139609, A276086, A324198.
%K A371099 nonn
%O A371099 0,1
%A A371099 _Antti Karttunen_, Mar 10 2024