A174425 Total number of divisors of all n-digit numbers.

23, 450, 6580, 86590, 1073071, 12803271, 148755315, 1694786187, 19020186047, 210925125565, 2316483913054, 25237165712764, 273094922940644, 2938181887791268, 31454145461543161, 335264720452385137, 3559879862893130917, 37671125212625723995, 397434517963203503069

Offset

1,1

Comments

Partial sums of A095256.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..36

Formula

From Andrew Howroyd, Jan 13 2020: (Start)

a(n) = A006218(10^n-1) - A006218(10^(n-1)-1).

a(n) = A057494(n) - A057494(n-1) - 2*n - 1. (End)

Example

For n = 1; a(1) = 23 because tau (r) of 1-digit numbers r = 1 to 9: {1, 2, 2, 3, 2, 4, 2, 4, 3}. Sum is 23.

Prog

(PARI) \\ too slow for n > 20; here b(n) is A006218(n).
b(n)={sum(k=1, sqrtint(n), n\k)*2 - sqrtint(n)^2}
a(n)={b(10^n-1)-b(10^(n-1)-1)} \\ Andrew Howroyd, Jan 13 2020

Crossrefs

Cf. A000005, A006218, A057494, A095256.

Sequence in context: A158453 A291128 A174262 * A076068 A062273 A066547

Adjacent sequences: A174422 A174423 A174424 * A174426 A174427 A174428

Keyword

nonn,base

Author

Jaroslav Krizek, Nov 28 2010

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 13 2020

Status

approved