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%I #44 Oct 23 2023 16:15:18
%S 1,27,482,7069,93668,1166750,13970034,162725364,1857511568,
%T 20877697634,231802823220,2548286736297,27785452449086,
%U 300880375389757,3239062263181054,34693207724724246,369957928177109416,3929837791070240368,41600963003695964400,439035480966899467508
%N a(n) = Sum_{k = 1..10^n} d(k) where d(n) = number of divisors of n (A000005).
%C 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
%H Henri Lifchitz, <a href="/A057494/b057494.txt">Table of n, a(n) for n = 0..36</a>
%H Terence Tao, Ernest Croot III, and Harald Helfgott, <a href="http://dx.doi.org/10.1090/S0025-5718-2011-02542-1">Deterministic methods to find primes</a>, Mathematics of Computation, 81 (2012), 1233-1246. <a href="http://arxiv.org/abs/1009.3956">arXiv:1009.3956</a>, [math.NT], 2010-2012.
%F a(n) = A006218(10^n). - _Max Alekseyev_, May 10 2009
%t k = s = 0; Do[ While[ k < 10^n, k++; s = s + DivisorSigma[ 0, k ] ]; Print[s], {n, 0, 8} ]
%o (PARI) a(n) = sum(k=1, 10^n, numdiv(k)); \\ _Michel Marcus_, Feb 19 2017
%o (Python)
%o from math import isqrt
%o 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
%Y Cf. A006218, A050226, A085567, A085829, A085831.
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Sep 21 2000
%E a(10)-a(16) from _Max Alekseyev_, Jan 25 2010
%E a(17)-a(19) from _Donovan Johnson_, Dec 26 2012
%E a(20)-a(27) from _Hiroaki Yamanouchi_, Sep 22 2015
%E a(28)-a(36) from _Henri Lifchitz_, Feb 19 2017
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