A374469 The odd part of gcd(n, A163511(n)).

1, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 1, 3, 1, 1, 3, 5, 1, 1, 1, 1, 1, 1, 1, 3, 1, 5, 9, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 5, 1, 1, 1, 1, 11, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 5, 1, 9, 1, 1, 5, 1, 7, 1, 1, 1, 27, 1, 1, 3, 5, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 105

Offset: 0

Author

Antti Karttunen, Aug 07 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..100000

Crossrefs

Cf. A000265, A006519, A007814, A163511, A364255, A364495 (fixed points).

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A364255(n) = gcd(n, A163511(n));
A374469(n) = A000265(A364255(n));

Formula

a(n) = A000265(A364255(n)) = A000265(gcd(n, A163511(n))).

For n >= 1, a(n) = A364255(n) / A006519(n).

For n >= 0, a(2*n) = a(n).