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 A153876 #24 Oct 23 2023 17:38:56
%S A153876 1,4,11,29,68,160,364,820,1813,3981,8674,18782,40387,86443,184232,
%T A153876 391188,827787,1746443,3674573,7712561,16151933,33757505,70422235,
%U A153876 146659055,304947023,633152157,1312820598,2718674046,5623413203,11618957217,23982175093,49452872529
%N A153876 a(n) = Sum_{i=2^(n-1)..2^n-1} sigma_0(i), sigma_0(i) number of divisors of n, n positive integer.
%C A153876 This sequence tells how many binary numbers with n digits are there in the multiplication matrix [1,...,2^n -1]x[1,...,2^n -1]. In general, counting how many base-B numbers of length n are there in the multiplication matrix [1,...,B^n -1]x[1,...,B^n -1] gives a(n)= sum_{i=B^(n-1),(B^n)-1} sigma_0(i). Besides this motivation it is interesting to see the behavior of partial sums of sigma_0(i) on growing intervals : a(n)= sum_{i=f(n-1),f(n)} sigma_0(i).
%H A153876 Chai Wah Wu, <a href="/A153876/b153876.txt">Table of n, a(n) for n = 1..76</a>
%F A153876 a(n) = A085831(n) - A085831(n-1)-1. - _R. J. Mathar_, Jan 05 2009
%F A153876 a(n) = Sum_{k>=1} k * A346730(n,k). - _Alois P. Heinz_, Aug 01 2021
%o A153876 (PARI) a(n) = sum(i=2^(n-1), 2^n-1, numdiv(i)); \\ _Michel Marcus_, Oct 10 2021
%o A153876 (Python)
%o A153876 from math import isqrt
%o A153876 def A153876(n): return ((t:=isqrt(b:=(1<<n-1)-1))+(s:=isqrt(a:=(1<<n)-1)))*(t-s)+(sum(a//k for k in range(1,s+1))-sum(b//k for k in range(1,t+1))<<1) # _Chai Wah Wu_, Oct 23 2023
%Y A153876 Cf. A000005, A006218, A095256, A140480, A346730.
%K A153876 nonn,easy
%O A153876 1,2
%A A153876 _Ctibor O. Zizka_, Jan 03 2009
%E A153876 a(14)-a(32) from _Alois P. Heinz_, Aug 01 2021