A353274 - OEIS

%I #7 Apr 13 2022 16:50:02

%S 1,2,3,1,5,2,7,1,1,2,11,1,13,2,3,1,17,2,19,5,3,2,23,1,1,2,1,7,29,2,31,

%T 1,3,2,5,1,37,2,3,5,41,6,43,11,1,2,47,3,1,2,3,13,53,2,5,7,3,2,59,1,61,

%U 2,7,1,5,2,67,17,3,2,71,1,73,2,3,19,7,2,79,5,1,2,83,1,5,2,3,11,89,2,7,23,3,2,5,3,97

%N a(n) = gcd(n, A353272(n)).

%H Antti Karttunen, <a href="/A353274/b353274.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = gcd(n, A353272(n)) = gcd(n, A353273(n)) = gcd(A353272(n), A353273(n)).

%F a(p) = p for all primes p.

%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 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 A332449(n) = A005940(1+(3*A156552(n)));

%o A353274(n) = { my(u=A332449(n)); gcd(n, (u / gcd(n, u))); };

%Y Cf. A005940, A156552, A332449, A353270, A353271, A353272, A353273.

%K nonn

%O 1,2

%A _Antti Karttunen_, Apr 09 2022