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A057494
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a(n) = Sum_{k = 1..10^n} d(k) where d(n) = number of divisors of n (A000005).
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9
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1, 27, 482, 7069, 93668, 1166750, 13970034, 162725364, 1857511568, 20877697634, 231802823220, 2548286736297, 27785452449086, 300880375389757, 3239062263181054, 34693207724724246, 369957928177109416, 3929837791070240368, 41600963003695964400, 439035480966899467508
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OFFSET
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0,2
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COMMENTS
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The Polymath project describes an algorithm for computing a(n) in time O(2.154...^n), see Tao, Croot, and Helfgott link. - Charles R Greathouse IV, Apr 16 2012
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LINKS
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FORMULA
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MATHEMATICA
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k = s = 0; Do[ While[ k < 10^n, k++; s = s + DivisorSigma[ 0, k ] ]; Print[s], {n, 0, 8} ]
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PROG
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(PARI) a(n) = sum(k=1, 10^n, numdiv(k)); \\ Michel Marcus, Feb 19 2017
(Python)
from math import isqrt
def A057494(n): return -(s:=isqrt(m:=10**n))**2+(sum(m//k for k in range(1, s+1))<<1) # Chai Wah Wu, Oct 23 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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