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 A230583 a(n) = floor(s(n) - n*(log(n) + 2*Gamma - 1)), where s(n) = sum_{k=1..n} tau(k), where tau(k) is the number of divisors of k. 1
 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 0, 3, 1, 1, 2, 3, 1, 3, 1, 2, 2, 2, 0, 4, 2, 2, 1, 3, 0, 4, 1, 3, 2, 1, 1, 5, 2, 1, 1, 4, 1, 4, 1, 2, 3, 2, -1, 4, 2, 3, 2, 3, 0, 3, 2, 4, 3, 2, -1, 6, 2, 1, 2, 3, 2, 5, 1, 2, 1, 3, 0, 6, 3, 2, 2, 3, 1, 4, 0, 5, 4, 2, -1, 5, 4, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Dirichlet proved this sequence is O(n^1/2). LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Wikipedia, Divisor summatory function Wikipedia, Euler-Mascheroni constant FORMULA a(n) = Sum(A000005(k), k=1..n) - n*(log(n) + 0.1544313298), where the decimal is (approximately) 2*Gamma-1. MATHEMATICA s = 0; Table[s = s + DivisorSigma[0, n]; Floor[s - n*(Log[n] + 2*EulerGamma - 1)], {n, 100}] (* T. D. Noe, Nov 04 2013 *) PROG (JavaScript) function sigma(n, k) { var j, s, sn; s=0; sn=Math.sqrt(n); for (j=1; j

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Last modified August 19 18:33 EDT 2019. Contains 326133 sequences. (Running on oeis4.)