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 A211780 #30 Jun 06 2024 03:48:45
%S A211780 0,2,2,7,2,14,2,18,9,18,2,43,2,22,20,41,2,54,2,57,24,30,2,106,13,34,
%T A211780 31,71,2,110,2,88,32,42,28,162,2,46,36,142,2,138,2,99,81,54,2,237,17,
%U A211780 102,44,113,2,178,36,178,48,66,2,325,2,70,99,183,40,194,2
%N A211780 a(n) = Sum_{d|n, d<n} d * tau(n / d), where tau = A000005 is the number of divisors.
%C A211780 Numbers n such that n divides a(n) are given in A068978.
%H A211780 Antti Karttunen, <a href="/A211780/b211780.txt">Table of n, a(n) for n = 1..27144</a> (first 1000 terms from Jaroslav Krizek)
%F A211780 a(n) = A007429(n) - n = A211779(n) + A000203(n) - n .
%F A211780 a(n) = (Sum_{d|n} A000203(d)) - n. - _Antti Karttunen_, Nov 13 2017
%F A211780 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Pi^4/36 - 1 = 1.705808... . - _Amiram Eldar_, Jun 06 2024
%e A211780 For n = 12: Sum_{d|n, d<n} d * tau(n / d) = 1*6 + 2*4 + 3*3 + 4*2 + 6*2 = 43.
%t A211780 Table[Sum[d*DivisorSigma[0, n/d], {d, Most[Divisors[n]]}], {n, 100}] (* _T. D. Noe_, Apr 27 2012 *)
%o A211780 (PARI) A211780(n) = sumdiv(n, d, sigma(d))-n; \\ _Antti Karttunen_, Nov 13 2017
%o A211780 (Python) A211780=lambda n:sum(sigma(d) for d in divisors(n, generator=True))-n
%o A211780 from sympy import divisor_sigma as sigma, divisors # _M. F. Hasler_, Jun 03 2024
%Y A211780 Cf. A000005, A000203, A007429, A068978, A098198, A211779.
%K A211780 nonn
%O A211780 1,2
%A A211780 _Jaroslav Krizek_, Apr 20 2012
%E A211780 Name edited by _M. F. Hasler_, Jun 03 2024