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A356151 Greatest common divisor of n and the smallest positive k such that n divides k*A276086(k), where A276086 is primorial base exp-function.

%I A356151 #11 Jul 28 2022 15:15:30
%S A356151 1,1,1,4,5,2,7,8,3,5,11,4,13,7,5,16,17,3,19,4,7,11,23,8,5,13,9,28,29,
%T A356151 5,31,32,11,17,7,4,37,19,13,8,41,14,43,44,5,23,47,16,7,10,17,52,53,9,
%U A356151 11,8,19,29,59,4,61,31,21,64,13,11,67,68,23,7,71,8,73,37,5,76,11,26,79,16,27,41,83,28,17,43,29,88
%N A356151 Greatest common divisor of n and the smallest positive k such that n divides k*A276086(k), where A276086 is primorial base exp-function.
%H A356151 Antti Karttunen, <a href="/A356151/b356151.txt">Table of n, a(n) for n = 1..65537</a>
%H A356151 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A356151 a(n) = gcd(n, A355944(n)) = gcd(n, A355945(n)) = gcd(A355944(n), A355945(n)).
%F A356151 a(n) = n / A356152(n) = A355944(n) / A356153(n).
%o A356151 (PARI)
%o A356151 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A356151 A356151(n) = for(k=1, oo, if((k*A276086(k))%n==0, return(gcd(n,k))));
%Y A356151 Cf. A276086, A324580, A355944, A355945, A356152, A356153.
%K A356151 nonn
%O A356151 1,4
%A A356151 _Antti Karttunen_, Jul 28 2022