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A353271 a(n) = n / gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).

%I A353271 #8 Apr 11 2022 20:48:18
%S A353271 1,1,1,2,1,3,1,4,3,5,1,6,1,7,5,8,1,9,1,2,7,11,1,4,5,13,9,2,1,15,1,16,
%T A353271 11,17,7,18,1,19,13,4,1,7,1,2,15,23,1,8,7,25,17,2,1,9,11,4,19,29,1,30,
%U A353271 1,31,3,32,13,33,1,2,23,35,1,12,1,37,25,2,11,39,1,8,27,41,1,42,17,43,29,4,1,45,13,2,31
%N A353271 a(n) = n / gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).
%H A353271 Antti Karttunen, <a href="/A353271/b353271.txt">Table of n, a(n) for n = 1..16384</a>
%H A353271 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353271 a(n) = n / A353270(n) = n / gcd(n, A005940(1+(3*A156552(n)))).
%o A353271 (PARI)
%o A353271 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A353271 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 A353271 A332449(n) = A005940(1+(3*A156552(n)));
%o A353271 A353271(n) = (n / gcd(n, A332449(n)));
%Y A353271 Cf. A005940, A156552, A332449, A353270.
%K A353271 nonn,less
%O A353271 1,4
%A A353271 _Antti Karttunen_, Apr 09 2022