A325632 a(n) = gcd(n, A325634(n)) = gcd(n, A091255(n, sigma(n))).

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 12, 1, 2, 1, 28, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 1, 10, 1, 2, 1, 4, 5, 2, 1, 4, 1, 1, 3, 2, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 1, 1, 6, 1, 2, 1, 14, 1, 9, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 28, 5, 2, 1, 4, 1, 2, 1, 4, 1, 2, 5, 12, 1, 1, 1, 1, 1, 2, 1, 2, 3

Offset: 1

Author

Antti Karttunen, May 21 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to polynomials in ring GF(2)[X]
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A091255, A325634, A325639 (fixed points).

Differs from A009194 for the first time at n=42, where a(42) = 2, while A009194(42) = 6.

Differs from A325633 and A325640 for the first time at n=45, where a(45) = 5, while A325633(45) = 1 and A325640(45) = 3.

Programs

PARI

A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);
A325634(n) = A091255sq(n, sigma(n));
A325632(n) = gcd(n,A325634(n));

Formula

a(n) = gcd(n, A325634(n)) = gcd(n, A091255(n, A000203(n))).