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

0,4

Links

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

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).

Prog

(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));

Crossrefs

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

Sequence in context: A251913 A285012 A139378 * A038500 A091840 A083985

Adjacent sequences: A374466 A374467 A374468 * A374470 A374471 A374472

Keyword

nonn

Author

Antti Karttunen, Aug 07 2024

Status

approved