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 A160399 #42 Sep 08 2022 08:45:45
%S A160399 1,4,11,27,62,137,296,630,1326,2768,5744,11867,24429,50135,102627,
%T A160399 209641,427518,870579,1770536,3596614,7298397,14796658,29974913,
%U A160399 60681233,122767148,248232863,501648844,1013257334,2045684971
%N A160399 a(n) = Sum_{k=1..n} binomial(n,k) * d(k), where d(k) = the number of positive divisors of k.
%C A160399 Binomial transform of the sequence d(n) (A000005). - _Emeric Deutsch_, May 15 2009
%C A160399 Apparently the partial sums of A101509. - _R. J. Mathar_, May 17 2009
%H A160399 Alois P. Heinz, <a href="/A160399/b160399.txt">Table of n, a(n) for n = 1..1000</a>
%H A160399 Eric M. Schmidt, <a href="https://dx.doi.org/10.1216/RMJ-2017-47-8-2777">The probability that the number of points on a complete intersection is squarefree</a>, Rocky Mountain J. Math, Volume 47, Number 8 (2017), 2777-2796.
%F A160399 G.f.: (Sum_{k>=1} (x/(1-x))^k/(1-x^k/(1-x)^k))/(1-x). - _Emeric Deutsch_, May 15 2009
%F A160399 E.g.f.: exp(x)*Sum_{k>=1} d(k)*x^k/k!. - _Ilya Gutkovskiy_, Nov 26 2017
%F A160399 a(n) = 2^n*(log(n) + 2*gamma - log(2)) + O(2^n*n^(-1/4)). [Put alpha_n = beta_n = 1/2 in Thm. 4.2 of Schmidt.] - _Eric M. Schmidt_, Feb 03 2018
%F A160399 a(n) = Sum_{i=1..n} Sum_{j=1..n} binomial(n,i*j). - _Ridouane Oudra_, Nov 12 2019
%p A160399 with(numtheory): seq(sum(binomial(n, k)*tau(k), k = 1 .. n), n = 1 .. 30); # _Emeric Deutsch_, May 15 2009
%p A160399 A160399 := proc(n) local k; add(binomial(n,k)*numtheory[tau](k),k=1..n) ; end: seq(A160399(n),n=1..40) ; # _R. J. Mathar_, May 17 2009
%t A160399 a[n_] := Sum[Binomial[n, k]*DivisorSigma[0, k], {k, 1, n}]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Feb 25 2017 *)
%o A160399 (PARI) a(n) = sum(k=1, n, binomial(n, k)*numdiv(k)); \\ _Michel Marcus_, Feb 25 2017
%o A160399 (GAP) List([1..10^3], n -> Sum([1..n], k -> Binomial(n,k) * Number(DivisorsInt(k)))); # _Muniru A Asiru_, Feb 04 2018
%o A160399 (Magma) [&+[Binomial(n,k)*NumberOfDivisors(k):k in [1..n]]:n in [1..30]]; // _Marius A. Burtea_, Nov 12 2019
%o A160399 (Magma) [&+[&+[Binomial(n,i*j):j in [1..n]]:i in [1..n]]:n in [1..31]]; // _Marius A. Burtea_, Nov 12 2019
%Y A160399 Cf. A000005. - _Emeric Deutsch_, May 15 2009
%Y A160399 Cf. A101509, A185003.
%K A160399 nonn
%O A160399 1,2
%A A160399 _Leroy Quet_, May 12 2009
%E A160399 More terms from _Emeric Deutsch_ and _R. J. Mathar_, May 15 2009