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A060436 Numerator of Sum_{k=1..n} d(k)/k, where d() = A000005().

%I A060436 #23 Aug 11 2025 09:02:03
%S A060436 1,2,8,41,229,269,2003,2213,2353,2521,28571,30881,410693,427853,
%T A060436 443869,1850551,31939847,33301207,640891093,664170349,226316943,
%U A060436 231019823,5365187609,16690477147,84523231511,85896110711,784963282799,802173304199,23423652688171
%N A060436 Numerator of Sum_{k=1..n} d(k)/k, where d() = A000005().
%C A060436 The old entry with this sequence number was a duplicate of A054845.
%D A060436 M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 237.
%H A060436 Robert Israel, <a href="/A060436/b060436.txt">Table of n, a(n) for n = 1..2296</a>
%H A060436 Vaclav Kotesovec, <a href="/A060436/a060436.jpg">Graph - The asymptotic ratio of Sum_{k=1..n} d(k)/k</a>
%H A060436 Mathematics.StackExchange, <a href="https://math.stackexchange.com/questions/471326/the-asymptotic-expansion-for-the-weighted-sum-of-divisors-sum-n-leq-x-frac">The asymptotic expansion for the weighted sum of divisors</a>, Aug 19 2013.
%F A060436 Sum_{k=1..n} A000005(k)/k = a(n)/A065080(n) ~ log(n)^2/2 + 2*gamma*log(n) + gamma^2 - 2*gamma_1, where gamma is the Euler-Mascheroni constant A001620 and gamma_1 is the first Stieltjes constant A082633. - _Vaclav Kotesovec_, Aug 30 2018
%e A060436 1, 2, 8/3, 41/12, 229/60, 269/60, 2003/420, 2213/420, 2353/420, 2521/420, 28571/4620, 30881/4620, ...
%p A060436 t:= 0:
%p A060436 for n from 1 to 50 do
%p A060436   t:= t + numtheory:-tau(n)/n;
%p A060436   A[n]:= numer(t);
%p A060436 od:
%p A060436 seq(A[n],n=1..50); # _Robert Israel_, Mar 20 2018
%Y A060436 Cf. A000005, A065080.
%K A060436 nonn,frac
%O A060436 1,2
%A A060436 _N. J. A. Sloane_, Nov 02 2008