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%I #24 Sep 11 2024 11:35:07
%S 1,4,6,12,8,96,8,64,20,256,96,2304,64,512,12288,5120,64,5120,8,6144,
%T 24576,3072,64,24576,1536,1024,7168,12288,256,3145728,32,98304,36864,
%U 2048,8192,491520,128,128,49152,131072,128,6291456,256,73728,5242880
%N a(n) is the number of divisors of N, where N = concatenation of n taken n times.
%H Max Alekseyev, <a href="/A110758/b110758.txt">Table of n, a(n) for n = 1..158</a>
%F a(n) = A000005(A000461(n)). - _Michel Marcus_, Nov 18 2018
%e a(3) = tau(333) = 6.
%t 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 *)
%t Table[DivisorSigma[0,FromDigits[Flatten[IntegerDigits/@PadRight[{},n,n]]]],{n,50}] (* _Harvey P. Dale_, Apr 10 2023 *)
%o (PARI) a(n) = numdiv(eval(concat(apply(x->Str(x), vector(n, k, n))))); \\ _Michel Marcus_, Feb 12 2023
%Y Cf. A000005, A000461.
%Y Cf. A110756, A110757, A110759, A110760.
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Aug 11 2005
%E Corrected and extended by _Ryan Propper_, Jul 21 2006