This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A212717 #17 Dec 25 2024 03:41:18
%S A212717 1,4,19,145,53,83,353,607,8171,75359,78089,79259,11657,2963,12047,
%T A212717 378137,386197,389917,397171,2804377,11344453,11457293,11626553,
%U A212717 11694257,11825297,11922017,12023573,12096113,12231521,12287941,6207443,6239683,3140999,9479417
%N A212717 Numerator of Sum_{k=1..n} 1/sigma(k).
%H A212717 Harvey P. Dale, <a href="/A212717/b212717.txt">Table of n, a(n) for n = 1..1000</a>
%H A212717 V. Sita Ramaiah and D. Suryanarayana, <a href="http://doi.org/10.18926/mjou/33820">Sums of reciprocals of some multiplicative functions</a>, Mathematical Journal of Okayama University, Vol. 21, No. 2 (1979), pp. 155-164.
%H A212717 László Tóth, <a href="https://www.emis.de/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1.
%F A212717 a(n)/A212718(n) = c * (log(n) + gamma + Sum_{p prime} (p-1)^2*beta(p)*log(p)/(p*alpha(p))) + O(log(n)^(2/3)*log(log(n))^(4/3)/n), where alpha(p) = 1 - ((p-1)^2/p) * Sum_{k>=1} 1/((p^k-1)*(p^(k+1)-1)), beta(p) = Sum_{k>=1} k/((p^k-1)*(p^(k+1)-1)), and c = Product_{p prime} alpha(p) = A308039 (Sita Ramaiah and Suryanarayana, 1979). - _Amiram Eldar_, Oct 16 2022
%e A212717 1, 4/3, 19/12, 145/84, 53/28, 83/42, 353/168, ...
%p A212717 with(numtheory): a:=n->numer(sum(1/sigma(k), k=1..n)): seq(a(n), n=1..50);
%t A212717 Numerator[Table[Sum[1/DivisorSigma[1,k],{k,1,n}],{n,1,50}]]
%t A212717 Accumulate[1/DivisorSigma[1,Range[40]]]//Numerator (* _Harvey P. Dale_, Aug 13 2023 *)
%Y A212717 Cf. A000203, A212718 (denominators), A308039, A345327.
%K A212717 nonn,frac
%O A212717 1,2
%A A212717 _Michel Lagneau_, May 25 2012