A110754 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.

36, 144, 768, 576, 1152, 6144, 2304, 18432, 15360, 18432, 12288, 49152, 4608, 36864, 6291456, 294912, 9216, 983040, 576, 294912, 18874368, 196608, 9216, 25165824, 1179648, 73728, 2359296, 1179648, 73728, 402653184, 2304, 2359296, 33554432, 147456, 75497472, 31457280, 147456, 36864

Offset: 1

Author

Amarnath Murthy, Aug 11 2005

Keywords

• base
• nonn

Comments

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

Examples

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

Crossrefs

Cf. A110751, A110752, A110753.

Programs

Maple

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

Mathematica

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

PARI

a(n)={numdiv(8712*(10^(4*n)-1)/9999)} \\ Andrew Howroyd, Nov 09 2019

Formula

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

Extensions

More terms from R. J. Mathar, Aug 17 2007

a(23)-a(38) from Andrew Howroyd, Nov 09 2019