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A353272 a(n) = A332449(n) / gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).

%I A353272 #9 Apr 13 2022 16:49:49
%S A353272 1,2,3,5,5,8,7,15,7,18,11,11,13,50,27,45,17,20,19,25,75,98,23,11,11,
%T A353272 242,35,35,29,32,31,135,147,338,125,77,37,578,363,75,41,24,43,55,13,
%U A353272 722,47,33,13,42,507,65,53,20,245,105,867,1058,59,17,61,1682,49,405,605,200,67,85,1083,162,71,77,73,1922,63
%N A353272 a(n) = A332449(n) / gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).
%H A353272 Antti Karttunen, <a href="/A353272/b353272.txt">Table of n, a(n) for n = 1..16384</a>
%H A353272 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353272 a(n) = A332449(n) / A353270(n) = A332449(n) / gcd(n, A332449(n)).
%F A353272 a(p) = p for all primes p.
%o A353272 (PARI)
%o A353272 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A353272 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 A353272 A332449(n) = A005940(1+(3*A156552(n)));
%o A353272 A353272(n) = { my(u=A332449(n)); (u / gcd(n, u)); };
%Y A353272 Cf. A005940, A156552, A332449, A353270, A353271, A353273, A353274 [= gcd(n, a(n))].
%K A353272 nonn,look
%O A353272 1,2
%A A353272 _Antti Karttunen_, Apr 09 2022