A353274 a(n) = gcd(n, A353272(n)).

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, 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, 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

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Formula

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

a(p) = p for all primes p.

Prog

(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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 };
A332449(n) = A005940(1+(3*A156552(n)));
A353274(n) = { my(u=A332449(n)); gcd(n, (u / gcd(n, u))); };

Crossrefs

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

Sequence in context: A323071 A340078 A126773 * A326691 A277698 A134194

Adjacent sequences: A353271 A353272 A353273 * A353275 A353276 A353277

Keyword

nonn

Author

Antti Karttunen, Apr 09 2022

Status

approved