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A324198 a(n) = gcd(n, A276086(n)), where A276086 is the primorial base exp-function.

%I A324198 #24 Mar 11 2024 18:05:39
%S A324198 1,1,1,3,1,1,1,1,1,3,5,1,1,1,1,15,1,1,1,1,5,3,1,1,1,25,1,3,1,1,1,1,1,
%T A324198 3,1,7,1,1,1,3,5,1,7,1,1,15,1,1,1,7,25,3,1,1,1,5,7,3,1,1,1,1,1,21,1,1,
%U A324198 1,1,1,3,35,1,1,1,1,75,1,7,1,1,5,3,1,1,7,5,1,3,1,1,1,7,1,3,1,1,1,1,49,3,5,1,1,1,1,105
%N A324198 a(n) = gcd(n, A276086(n)), where A276086 is the primorial base exp-function.
%H A324198 Antti Karttunen, <a href="/A324198/b324198.txt">Table of n, a(n) for n = 0..65537</a>
%H A324198 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A324198 a(n) = gcd(n, A276086(n)).
%F A324198 From _Antti Karttunen_, Oct 21 2019: (Start)
%F A324198 A000005(a(n)) = A327168(n).
%F A324198 a(A328316(n)) = A328323(n).
%F A324198 a(n) = A324580(n) / A328584(n).
%F A324198 (End)
%t A324198 Array[Block[{i, m, n = #, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; GCD[#, m]] &, 106, 0] (* _Michael De Vlieger_, Feb 04 2022 *)
%o A324198 (PARI)
%o A324198 A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
%o A324198 A324198(n) = gcd(n,A276086(n));
%o A324198 (PARI) 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); }; \\ _Antti Karttunen_, Oct 21 2019
%Y A324198 Cf. A003989, A276086, A323878, A324284, A324350, A324351, A324384, A324577, A324580, A324646, A327858, A328323, A327168, A328316, A328323, A328386, A328584, A346242 (Dirichlet inverse), A351254.
%Y A324198 Cf. A324583 (positions of ones), A324584 (and terms larger than one).
%Y A324198 Cf. A371098 (odd bisection), A371099 [= a(36n+9)].
%Y A324198 Cf. also A328231.
%K A324198 nonn
%O A324198 0,4
%A A324198 _Antti Karttunen_, Feb 25 2019