login
a(n) = tau(n)^omega(n), where tau = A000005 and omega = A001221.
7

%I #12 Sep 15 2024 02:41:06

%S 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,

%T 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,

%U 64,16,64,16,16,2,1728,2,16,36,7,16,512,2,36,16,512,2,144,2,16,36,36,16

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

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

%H Reinhard Zumkeller, <a href="/A110088/b110088.txt">Table of n, a(n) for n = 1..10000</a>

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

%t a[n_] := DivisorSigma[0, n]^PrimeNu[n]; Array[a, 100] (* _Amiram Eldar_, Sep 15 2024 *)

%o (Haskell)

%o a110088 n = a000005 n ^ a001221 n -- _Reinhard Zumkeller_, Aug 05 2014

%o (PARI) a(n) = {my(f = factor(n)); numdiv(f)^omega(f);} \\ _Amiram Eldar_, Sep 15 2024

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

%K nonn,easy

%O 1,2

%A _Reinhard Zumkeller_, Jul 11 2005