cp's OEIS Frontend

A353270 a(n) = gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).

%I A353270 #10 Apr 13 2022 16:49:40
%S A353270 1,2,3,2,5,2,7,2,3,2,11,2,13,2,3,2,17,2,19,10,3,2,23,6,5,2,3,14,29,2,
%T A353270 31,2,3,2,5,2,37,2,3,10,41,6,43,22,3,2,47,6,7,2,3,26,53,6,5,14,3,2,59,
%U A353270 2,61,2,21,2,5,2,67,34,3,2,71,6,73,2,3,38,7,2,79,10,3,2,83,2,5,2,3,22,89,2,7,46,3,2,5,6
%N A353270 a(n) = gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).
%H A353270 Antti Karttunen, <a href="/A353270/b353270.txt">Table of n, a(n) for n = 1..16384</a>
%H A353270 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353270 a(n) = gcd(n, A332449(n)) = gcd(n, A005940(1+(3*A156552(n)))).
%F A353270 a(n) = n / A353271(n) = A332449(n) / A353272(n).
%o A353270 (PARI)
%o A353270 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A353270 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 A353270 A332449(n) = A005940(1+(3*A156552(n)));
%o A353270 A353270(n) = gcd(n, A332449(n));
%Y A353270 Cf. A005940, A156552, A332449, A353271, A353272, A353274.
%K A353270 nonn
%O A353270 1,2
%A A353270 _Antti Karttunen_, Apr 09 2022