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a(n) = A163511(n) / gcd(n, A163511(n)).
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%I #13 Jul 27 2023 08:18:28

%S 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 21,7,11,2,81,81,125,3,375,125,343,9,225,25,245,25,49,49,121,1,135,9,

%U 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 a(n) = A163511(n) / gcd(n, A163511(n)).

%C Denominator of n / A163511(n).

%H Antti Karttunen, <a href="/A364492/b364492.txt">Table of n, a(n) for n = 0..16383</a>

%F a(n) = A163511(n) / A364255(n) = A163511(n) / gcd(n, A163511(n)).

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

%o A054429(n) = ((3<<#binary(n\2))-n-1);

%o A163511(n) = if(!n,1,A005940(1+A054429(n)))

%o A364492(n) = { my(u=A163511(n)); (u/gcd(n, u)); };

%o (Python)

%o from math import gcd

%o from sympy import nextprime

%o def A364492(n):

%o c, p, k = 1, 1, n

%o while k:

%o c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())

%o k >>= s+1

%o return c*p//gcd(c*p,n) # _Chai Wah Wu_, Jul 26 2023

%Y Cf. A163511, A364255, A364491 (numerators), A364493, A364496 (positions of 1's).

%K nonn,frac

%O 0,2

%A _Antti Karttunen_, Jul 26 2023