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 A245211 #23 Nov 10 2024 05:45:40
%S A245211 0,1,1,5,1,11,1,17,7,15,1,47,1,19,17,49,1,62,1,67,21,27,1,151,11,31,
%T A245211 34,87,1,145,1,129,29,39,25,254,1,43,33,219,1,189,1,127,104,51,1,423,
%U A245211 15,130,41,147,1,278,33,287,45,63,1,589,1,67,132,321,37,277
%N A245211 a(n) = Sum_{(d<n) | n} (d * tau(d)).
%C A245211 If q are proper divisors of n then values of sequence a(n) are the bending moments at point 0 of static forces of sizes tau(q) operating in places q on the cantilever as the nonnegative number axis of length n with support at point 0 by the schema: a(n) = Sum_{q | n} (q * tau(q)).
%C A245211 Number n = 144 is the smallest number n such that a(n) > n * tau(n) (see A245212 and A245214).
%C A245211 Conjecture: 21 is only number such that a(n) = n.
%H A245211 Jens Kruse Andersen, <a href="/A245211/b245211.txt">Table of n, a(n) for n = 1..10000</a>
%F A245211 a(n) = A060640(n) - A038040(n) = Sum_{d | n} (d * tau(d)) - n*tau(n).
%F A245211 a(n) = A038040(n) - A245212(n).
%F A245211 a(n) = 1 for n = primes.
%F A245211 a(n) = n + 5 for even semiprimes q = 2p > 4 (see A100484) where p = odd prime.
%e A245211 For n = 21 with proper divisors [1, 3, 7] we have: a(21) = 7 * tau(7) + 3 * tau(3) + 1 * tau(1) = 7*2 + 3*2 + 1*1 = 21.
%o A245211 (Magma) [(&+[d*#([e: e in Divisors(d)]): d in Divisors(n)])-(n*(#[d: d in Divisors(n)])): n in [1..1000]];
%o A245211 (PARI) a(n) = sumdiv(n, d, (d<n)*d*numdiv(d)) \\ _Jens Kruse Andersen_, Aug 13 2014
%Y A245211 Cf. A000005, A100484, A245212, A245213, A245214.
%K A245211 nonn
%O A245211 1,4
%A A245211 _Jaroslav Krizek_, Jul 23 2014