A070528 Number of divisors of 10^n-1 (999...999 with n digits).

3, 6, 8, 12, 12, 64, 12, 48, 20, 48, 12, 256, 24, 48, 128, 192, 12, 640, 6, 384, 256, 288, 6, 2048, 96, 192, 96, 768, 96, 16384, 24, 6144, 128, 192, 384, 5120, 24, 24, 128, 6144, 48, 49152, 48, 4608, 1280, 192, 12, 16384, 48, 3072, 512, 1536, 48, 12288, 768

Offset: 1

Author

Henry Bottomley, May 02 2002

Keywords

• base
• nonn

Examples

			a(7)=12 since the divisors of 9999999 are 1, 3, 9, 239, 717, 2151, 4649, 13947, 41841, 1111111, 3333333, 9999999.
		

Links

• Table of n, a(n) for n = 1..352

Crossrefs

Cf. A004023 (indices of 6's).

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895.

Cf. A046801, A005422, A102347, A046053, A057951, A007138, A003060, A059892, A085035.

Programs

Mathematica

DivisorSigma[0,#]&/@(10^Range[60]-1) (* Harvey P. Dale, Jan 14 2011 *)
Table[DivisorSigma[0, 10^n - 1], {n, 60}] (* T. D. Noe, Aug 18 2011 *)

PARI

a(n) = numdiv(10^n - 1); \\ Michel Marcus, Sep 08 2015

Formula

a(n) = A000005(A002283(n)).

a(n) = Sum_{d|n} A059892(d).

a(n) = A070529(n)*(A007949(n)+3)/(A007949(n)+1).

Extensions

Terms to a(280) in b-file from Hans Havermann, Aug 19 2011

a(281)-a(322) in b-file from Ray Chandler, Apr 22 2017

a(323)-a(352) in b-file from Max Alekseyev, May 04 2022