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A057494 a(n) = Sum_{k = 1..10^n} d(k) where d(n) = number of divisors of n (A000005). 9
1, 27, 482, 7069, 93668, 1166750, 13970034, 162725364, 1857511568, 20877697634, 231802823220, 2548286736297, 27785452449086, 300880375389757, 3239062263181054, 34693207724724246, 369957928177109416, 3929837791070240368, 41600963003695964400, 439035480966899467508 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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
LINKS
Terence Tao, Ernest Croot III, and Harald Helfgott, Deterministic methods to find primes, Mathematics of Computation, 81 (2012), 1233-1246. arXiv:1009.3956, [math.NT], 2010-2012.
FORMULA
a(n) = A006218(10^n). - Max Alekseyev, May 10 2009
MATHEMATICA
k = s = 0; Do[ While[ k < 10^n, k++; s = s + DivisorSigma[ 0, k ] ]; Print[s], {n, 0, 8} ]
PROG
(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
CROSSREFS
Sequence in context: A026543 A028046 A109821 * A024439 A026006 A024346
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 21 2000
EXTENSIONS
a(10)-a(16) from Max Alekseyev, Jan 25 2010
a(17)-a(19) from Donovan Johnson, Dec 26 2012
a(20)-a(27) from Hiroaki Yamanouchi, Sep 22 2015
a(28)-a(36) from Henri Lifchitz, Feb 19 2017
STATUS
approved

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Last modified June 24 22:33 EDT 2024. Contains 373690 sequences. (Running on oeis4.)