A082902 a(n) = gcd(2^n, sigma(2,n)) = gcd(A000079(n), A001157(n)).

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 4, 1, 2, 1, 2, 2, 4, 2, 2, 2, 1, 2, 4, 2, 2, 4, 2, 1, 4, 2, 4, 1, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 2, 1, 1, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 2, 2, 1, 4, 4, 2, 2, 4, 4, 2, 1, 2, 2, 2, 2, 4, 4, 2, 2, 1, 2, 2, 4, 4, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 2, 1, 2, 1, 2, 4, 2, 2, 8

Offset: 1

Author

Labos Elemer, Apr 22 2003

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000079, A001157, A006519.

Programs

Mathematica

a[n_] := 2^IntegerExponent[DivisorSigma[2, n], 2]; Array[a, 100] (* Amiram Eldar, Oct 01 2023 *)

PARI

A082902(n) = gcd(2^n, sigma(n, 2)); \\ Antti Karttunen, Sep 27 2018

Formula

a(n) = A006519(A001157(n)). - Antti Karttunen, Sep 27 2018

Multiplicative with a(2^e) = 1, and a(p^e) = A006519(e+1) for an odd prime p. - Amiram Eldar, Oct 01 2023