A303781 a(2) = 1; for n <> 2, a(n) = gcd(n, A000005(n)), where A000005(n) = number of divisors of n.

1, 1, 1, 1, 1, 2, 1, 4, 3, 2, 1, 6, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 9, 1, 2, 1, 8, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 8, 1, 2, 1, 12, 1, 2, 3, 1, 1, 2, 1, 2, 1, 2, 1, 12, 1, 2, 3, 2, 1, 2, 1, 10, 1, 2, 1, 12, 1, 2, 1, 8, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 3, 1, 1, 2, 1, 8, 1

Offset: 1

Author

Antti Karttunen, Apr 30 2018

Keywords

• nonn

Comments

Except for a(2) = 1, a(n) = A009191(n).

Links

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

Crossrefs

Cf. A000005, A009191.

Programs

Mathematica

Join[{1,1},Table[GCD[n,DivisorSigma[0,n]],{n,3,110}]] (* Harvey P. Dale, Mar 20 2023 *)

PARI

A303781(n) = if(2==n,1,gcd(n,numdiv(n)));

Formula

a(2) = 1; for n <> 2, a(n) = gcd(n, A000005(n)).