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A364491 a(n) = n / gcd(n, A163511(n)).

%I A364491 #15 Jul 27 2023 08:18:23
%S A364491 0,1,1,1,1,5,1,7,1,1,5,11,1,13,7,15,1,17,1,19,5,7,11,23,1,5,13,27,7,
%T A364491 29,15,31,1,11,17,7,1,37,19,39,5,41,7,43,11,15,23,47,1,49,5,51,13,53,
%U A364491 27,5,7,19,29,59,15,61,31,63,1,65,11,67,17,23,7,71,1,73,37,15,19,11,39,79,5,3,41,83,7,17,43,87
%N A364491 a(n) = n / gcd(n, A163511(n)).
%C A364491 Numerator of n / A163511(n).
%H A364491 Antti Karttunen, <a href="/A364491/b364491.txt">Table of n, a(n) for n = 0..16383</a>
%F A364491 a(n) = n / A364255(n) = n /  gcd(n, A163511(n)).
%o A364491 (PARI)
%o A364491 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A364491 A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
%o A364491 A163511(n) = if(!n,1,A005940(1+A054429(n)))
%o A364491 A364491(n) = (n/gcd(n, A163511(n)));
%o A364491 (Python)
%o A364491 from math import gcd
%o A364491 from sympy import nextprime
%o A364491 def A364491(n):
%o A364491     c, p, k = 1, 1, n
%o A364491     while k:
%o A364491         c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
%o A364491         k >>= s+1
%o A364491     return n//gcd(c*p,n) # _Chai Wah Wu_, Jul 26 2023
%Y A364491 Cf. A163511, A364255, A364492 (denominators), A364493, A364494 (positions of 1's).
%K A364491 nonn,frac
%O A364491 0,6
%A A364491 _Antti Karttunen_, Jul 26 2023