A339899 a(n) = gcd(A019565(2n)-1, A000265(phi(A019565(2n)))).

1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 5, 3, 1, 3, 1, 1, 1, 9, 1, 1, 1, 1, 1, 3, 1, 5, 1, 9, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 15, 1, 1, 1, 3, 5, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 1, 1, 3, 1, 3, 1, 1, 1, 27, 1, 1, 1, 1, 5, 3, 1, 1, 1, 81, 1, 1, 1, 3, 1, 1, 1, 9, 1, 3, 1

Offset: 0

Author

Antti Karttunen, Dec 28 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Crossrefs

Cf. A000010, A000265, A049559, A053575, A019565, A339809, A339821, A339971, A339898, A339901.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A339899(n) = { my(x=A019565(2*n)); gcd((x-1),A000265(eulerphi(x))); };

Formula

a(n) = gcd(A339809(2*n), A339971(n)), where A339971(n) = A053575(A019565(2n)).

a(n) = gcd(A339971(n), A339898(n)).

a(n) = A339971(n) / A339901(n).

a(n) = A000265(A049559(A019565(2*n))).