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 A061202 #37 Feb 16 2025 08:32:44
%S A061202 1,5,9,19,23,39,43,63,73,89,93,133,137,153,169,204,208,248,252,292,
%T A061202 308,324,328,408,418,434,454,494,498,562,566,622,638,654,670,770,774,
%U A061202 790,806,886,890,954,958,998,1038,1054,1058,1198,1208,1248,1264,1304,1308
%N A061202 (tau<=)_4(n).
%C A061202 (tau<=)_k(n) = |{(x_1,x_2,...,x_k): x_1*x_2*...*x_k <= n}|, i.e., (tau<=)_k(n) is number of solutions to x_1*x_2*...*x_k <= n, x_i > 0.
%C A061202 Partial sums of A007426.
%C A061202 Equals row sums of triangle A140703. - _Gary W. Adamson_, May 24 2008
%H A061202 Vaclav Kotesovec, <a href="/A061202/b061202.txt">Table of n, a(n) for n = 1..10000</a>
%H A061202 Vaclav Kotesovec, <a href="/A061202/a061202.jpg">Graph - The asymptotic ratio (1000000 terms)</a>
%H A061202 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StieltjesConstants.html">Stieltjes Constants</a>
%H A061202 Wikipedia, <a href="http://en.wikipedia.org/wiki/Stieltjes_constants">Stieltjes constants</a>
%F A061202 (tau<=)_k(n) = Sum_{i=1..n} tau_k(i).
%F A061202 a(n) = Sum_{k = 1..n} tau_{3}(k)*floor (n/k), where tau_{3} is A007425. - _Enrique Pérez Herrero_, Jan 23 2013
%F A061202 a(n) ~ n * (log(n)^3/6 + (2*g - 1/2)*log(n)^2 + (6*g^2 - 4*g - 4*g1 + 1)*log(n) + 4*g^3 - 6*g^2 + 4*g + 4*g1*(1 - 3*g) + 2*g2 - 1), where g is the Euler-Mascheroni constant A001620, g1 and g2 are the Stieltjes constants, see A082633 and A086279. - _Vaclav Kotesovec_, Sep 09 2018
%F A061202 a(n) = Sum_{i=1..n} tau(i)*A006218(floor(n/i)). - _Ridouane Oudra_, Sep 17 2021
%F A061202 a(n) = Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} floor(n/(i*j*k)). - _Ridouane Oudra_, Oct 31 2022
%t A061202 (* Asymptotics: *) n * (Log[n]^3/6 + (2*EulerGamma - 1/2)*Log[n]^2 + (6*EulerGamma^2 - 4*EulerGamma - 4*StieltjesGamma[1] + 1)*Log[n] + 4*EulerGamma^3 - 6*EulerGamma^2 + 4*EulerGamma + 4*StieltjesGamma[1]*(1 - 3*EulerGamma) + 2*StieltjesGamma[2] - 1) (* _Vaclav Kotesovec_, Sep 09 2018 *)
%Y A061202 Cf. tau_2(n): A000005, tau_3(n): A007425, tau_4(n): A007426, tau_5(n): A061200, tau_6(n): A034695, (unordered) 2-factorizations of n: A038548, (unordered) 3-factorizations of n: A034836, A001055, (tau<=)_2(n): A006218, (tau<=)_3(n): A061201, (tau<=)_5(n): A061203, (tau<=)_6(n): A061204.
%Y A061202 Equals left column of triangle A140705.
%Y A061202 Cf. A140703.
%K A061202 easy,nonn
%O A061202 1,2
%A A061202 _Vladeta Jovovic_, Apr 21 2001