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A364492 a(n) = A163511(n) / gcd(n, A163511(n)).

%I A364492 #13 Jul 27 2023 08:18:28
%S A364492 1,2,2,1,2,9,1,5,2,3,9,25,1,15,5,7,2,81,3,125,9,25,25,49,1,9,15,35,5,
%T A364492 21,7,11,2,81,81,125,3,375,125,343,9,225,25,245,25,49,49,121,1,135,9,
%U A364492 175,15,105,35,7,5,21,21,55,7,33,11,13,2,729,81,3125,81,625,125,2401,3,1125,375,343,125,147,343,1331
%N A364492 a(n) = A163511(n) / gcd(n, A163511(n)).
%C A364492 Denominator of n / A163511(n).
%H A364492 Antti Karttunen, <a href="/A364492/b364492.txt">Table of n, a(n) for n = 0..16383</a>
%F A364492 a(n) = A163511(n) / A364255(n) = A163511(n) / gcd(n, A163511(n)).
%o A364492 (PARI)
%o A364492 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A364492 A054429(n) = ((3<<#binary(n\2))-n-1);
%o A364492 A163511(n) = if(!n,1,A005940(1+A054429(n)))
%o A364492 A364492(n) = { my(u=A163511(n)); (u/gcd(n, u)); };
%o A364492 (Python)
%o A364492 from math import gcd
%o A364492 from sympy import nextprime
%o A364492 def A364492(n):
%o A364492     c, p, k = 1, 1, n
%o A364492     while k:
%o A364492         c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
%o A364492         k >>= s+1
%o A364492     return c*p//gcd(c*p,n) # _Chai Wah Wu_, Jul 26 2023
%Y A364492 Cf. A163511, A364255, A364491 (numerators), A364493, A364496 (positions of 1's).
%K A364492 nonn,frac
%O A364492 0,2
%A A364492 _Antti Karttunen_, Jul 26 2023