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

1,1

Comments

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

Links

Table of n, a(n) for n=1..38.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A110751, A110752, A110753.

Sequence in context: A005017 A288488 A262789 * A299854 A154711 A162992

Adjacent sequences: A110751 A110752 A110753 * A110755 A110756 A110757

Keyword

base,nonn

Author

Amarnath Murthy, Aug 11 2005

Extensions

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

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

Status

approved