A110088 a(n) = tau(n)^omega(n), where tau = A000005 and omega = A001221.

1, 2, 2, 3, 2, 16, 2, 4, 3, 16, 2, 36, 2, 16, 16, 5, 2, 36, 2, 36, 16, 16, 2, 64, 3, 16, 4, 36, 2, 512, 2, 6, 16, 16, 16, 81, 2, 16, 16, 64, 2, 512, 2, 36, 36, 16, 2, 100, 3, 36, 16, 36, 2, 64, 16, 64, 16, 16, 2, 1728, 2, 16, 36, 7, 16, 512, 2, 36, 16, 512, 2, 144, 2, 16, 36, 36, 16

Offset: 1

Author

Reinhard Zumkeller, Jul 11 2005

Keywords

• nonn
• easy

Comments

a(n) depends only on the prime signature of n.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A001221, A110085, A110086, A110087, A240960.

Programs

Haskell

a110088 n = a000005 n ^ a001221 n  -- Reinhard Zumkeller, Aug 05 2014

Mathematica

a[n_] := DivisorSigma[0, n]^PrimeNu[n]; Array[a, 100] (* Amiram Eldar, Sep 15 2024 *)

PARI

a(n) = {my(f = factor(n)); numdiv(f)^omega(f);} \\ Amiram Eldar, Sep 15 2024

Formula

a(n) = A000005(n)^A001221(n).