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A353275 a(n) = n / gcd(n, A353272(n)).

%I A353275 #9 Apr 11 2022 20:48:30
%S A353275 1,1,1,4,1,3,1,8,9,5,1,12,1,7,5,16,1,9,1,4,7,11,1,24,25,13,27,4,1,15,
%T A353275 1,32,11,17,7,36,1,19,13,8,1,7,1,4,45,23,1,16,49,25,17,4,1,27,11,8,19,
%U A353275 29,1,60,1,31,9,64,13,33,1,4,23,35,1,72,1,37,25,4,11,39,1,16,81,41,1,84,17,43,29,8,1,45,13
%N A353275 a(n) = n / gcd(n, A353272(n)).
%H A353275 Antti Karttunen, <a href="/A353275/b353275.txt">Table of n, a(n) for n = 1..10000</a>
%H A353275 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353275 a(n) = n / A353274(n) = n / gcd(n, A353272(n)).
%o A353275 (PARI)
%o A353275 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A353275 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A353275 A332449(n) = A005940(1+(3*A156552(n)));
%o A353275 A353275(n) = { my(u=A332449(n)); (n / gcd(n, (u / gcd(n, u)))); };
%Y A353275 Cf. A332449, A353272, A353273, A353274.
%K A353275 nonn,less
%O A353275 1,4
%A A353275 _Antti Karttunen_, Apr 10 2022