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A351084 a(n) = gcd(n, A328572(n)), where A328572 converts the primorial base expansion of n into its prime product form, but with 1 subtracted from all nonzero digits.

%I A351084 #14 Feb 04 2022 16:09:12
%S A351084 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,5,1,1,1,1,25,1,1,1,1,1,1,1,1,
%T A351084 1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,25,1,1,1,1,5,1,1,1,1,1,1,1,7,1,1,1,1,
%U A351084 1,1,7,1,1,1,1,5,1,7,1,1,5,1,1,1,7,5,1,1,1,1,1,7,1,1,1,1,1,1,49,1,1,1,1,1,1,35
%N A351084 a(n) = gcd(n, A328572(n)), where A328572 converts the primorial base expansion of n into its prime product form, but with 1 subtracted from all nonzero digits.
%H A351084 Antti Karttunen, <a href="/A351084/b351084.txt">Table of n, a(n) for n = 0..65537</a>
%H A351084 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A351084 a(n) = gcd(n, A328572(n)) = gcd(A324198(n), A351083(n)).
%F A351084 a(n) = gcd(n, A085731(A276086(n))) = gcd(n, A276086(n), A327860(n)).
%o A351084 (PARI)
%o A351084 A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
%o A351084 A351084(n) = gcd(n, A328572(n));
%o A351084 (PARI) A351084(n) = { my(m=1, p=2, orgn=n); while(n, if(n%p, m *= (p^min((n%p)-1, valuation(orgn, p)))); n = n\p; p = nextprime(1+p)); (m); };
%Y A351084 Cf. A003415, A276086, A324198, A327860, A328572, A351080, A351083.
%K A351084 nonn,easy
%O A351084 0,16
%A A351084 _Antti Karttunen_, Feb 03 2022