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 A244824 #26 Oct 24 2023 00:54:48 %S A244824 1,4,15,56,220,857,3403,13535,54077,215900,862954,3450545,13802279, %T A244824 55201838,220792018,883134861,3532518195,14129951284,56519699688, %U A244824 226078355122,904312961284,3617249936000,14468996179294,57875977567596,231503907383054,926015589350438 %N A244824 Sum of all divisors of all positive integers <= 2^n. %C A244824 Has a symmetric representation, the same as A024916. %H A244824 Chai Wah Wu, <a href="/A244824/b244824.txt">Table of n, a(n) for n = 0..75</a> %F A244824 a(n) = A024916(A000079(n)). %F A244824 a(n) ~ 2^(2*n-2) * Pi^2/3. - _Vaclav Kotesovec_, Oct 23 2023 %e A244824 For n = 2 the sum of all divisors of all positive integers <= 4 is [1] + [1+2] + [1+3] + [1+2+4] = 1 + 3 + 4 + 7 = 15, so a(2) = 15. %o A244824 (PARI) a(n) = sum(k=1, 2^n, k*floor(2^n/k) ) \\ _Jens Kruse Andersen_, Jul 26 2014 %o A244824 (Python) %o A244824 from math import isqrt %o A244824 def A244824(n): return -(s:=isqrt(m:=1<<n))**2*(s+1) + sum((q:=m//k)*((k<<1)+q+1) for k in range(1,s+1))>>1 # _Chai Wah Wu_, Oct 23 2023 %Y A244824 Cf. A000079, A000203, A024916, A196020, A235796, A236104, A237270, A237593. %K A244824 nonn %O A244824 0,2 %A A244824 _Omar E. Pol_, Jul 06 2014 %E A244824 More terms from _Jens Kruse Andersen_, Jul 26 2014