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

Author

Jaroslav Krizek, Nov 28 2010

Keywords

• nonn
• base

Comments

Partial sums are A095256.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005, A006218, A057494, A095256.

Programs

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

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)

Extensions

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