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A174425
Total number of divisors of all n-digit numbers.
2
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
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
KEYWORD
nonn,base
AUTHOR
Jaroslav Krizek, Nov 28 2010
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jan 13 2020
STATUS
approved