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

1,1

Links

Table of n, a(n) for n = 1..352

Formula

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

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

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

Example

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

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 *)

Prog

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

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.

Sequence in context: A233541 A077148 A246456 * A243117 A356180 A122116

Adjacent sequences: A070525 A070526 A070527 * A070529 A070530 A070531

Keyword

base,nonn

Author

Henry Bottomley, May 02 2002

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

Status

approved