A110758 a(n) is the number of divisors of N, where N = concatenation of n taken n times.

1, 4, 6, 12, 8, 96, 8, 64, 20, 256, 96, 2304, 64, 512, 12288, 5120, 64, 5120, 8, 6144, 24576, 3072, 64, 24576, 1536, 1024, 7168, 12288, 256, 3145728, 32, 98304, 36864, 2048, 8192, 491520, 128, 128, 49152, 131072, 128, 6291456, 256, 73728, 5242880

Offset: 1

Author

Amarnath Murthy, Aug 11 2005

Keywords

• base
• nonn

Examples

			a(3) = tau(333) = 6.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..158

Crossrefs

Cf. A000005, A000461.

Cf. A110756, A110757, A110759, A110760.

Programs

Mathematica

f[n_] := Sum[n*10^(i * Length[IntegerDigits[n]]), {i, 0, n - 1}]; Do[Print[DivisorSigma[0, f[n]]], {n, 100}] (* Ryan Propper, Jul 21 2006 *)
Table[DivisorSigma[0,FromDigits[Flatten[IntegerDigits/@PadRight[{},n,n]]]],{n,50}] (* Harvey P. Dale, Apr 10 2023 *)

PARI

a(n) = numdiv(eval(concat(apply(x->Str(x), vector(n, k, n))))); \\ Michel Marcus, Feb 12 2023

Formula

a(n) = A000005(A000461(n)). - Michel Marcus, Nov 18 2018

Extensions

Corrected and extended by Ryan Propper, Jul 21 2006