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a(n) = tau(N), where N = the number obtained as a concatenation of 8712 with itself n times and tau(n) = number of divisors of n.
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%I #14 Nov 09 2019 16:27:09

%S 36,144,768,576,1152,6144,2304,18432,15360,18432,12288,49152,4608,

%T 36864,6291456,294912,9216,983040,576,294912,18874368,196608,9216,

%U 25165824,1179648,73728,2359296,1179648,73728,402653184,2304,2359296,33554432,147456,75497472,31457280,147456,36864

%N a(n) = tau(N), where N = the number obtained as a concatenation of 8712 with itself n times and tau(n) = number of divisors of n.

%C 8712 has the property that any number of concatenation of it with self and the digit reversal have same prime divisors.

%F a(n) = A000005(8712*Sum_{i=0..n-1} 10^(4i)). - _R. J. Mathar_, Aug 17 2007

%e a(2) = tau(87128712) = 144.

%p A110754 := proc(n) local pow8712,i ; pow8712 := 8712*add(10^(4*i),i=0..n-1) ; numtheory[tau](pow8712) ; end: seq(A110754(n),n=1..22) ; # _R. J. Mathar_, Aug 17 2007

%t Table[DivisorSigma[0,FromDigits[PadRight[{},4n,{8,7,1,2}]]],{n,25}] (* _Harvey P. Dale_, Dec 29 2016 *)

%o (PARI) a(n)={numdiv(8712*(10^(4*n)-1)/9999)} \\ _Andrew Howroyd_, Nov 09 2019

%Y Cf. A110751, A110752, A110753.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Aug 11 2005

%E More terms from _R. J. Mathar_, Aug 17 2007

%E a(23)-a(38) from _Andrew Howroyd_, Nov 09 2019