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 A238952 #44 May 02 2025 23:36:42
%S A238952 0,1,1,3,1,5,1,6,3,5,1,12,1,5,5,10,1,12,1,12,5,5,1,22,3,5,6,12,1,19,1,
%T A238952 15,5,5,5,27,1,5,5,22,1,19,1,12,12,5,1,35,3,12,5,12,1,22,5,22,5,5,1,
%U A238952 42,1,5,12,21,5,19,1,12,5,19,1,48,1,5,12,12,5
%N A238952 The size (the number of arcs) in the transitive closure of divisor lattice D(n).
%C A238952 a(n) is the number of ordered factorizations of n = r*s*t such that t is not equal to 1. For example: a(4)=3 because we have: 1*1*4, 1*2*2, and 2*1*2. Cf. A007425. - _Geoffrey Critzer_, Jan 01 2015
%C A238952 Number of pairs (d1, d2) of divisors of n such that d1<=d2, d1|n, d2|n, d1|d2 and d1 + d2 <= n. For example, a(8) has 6 divisor pairs (1,1), (1,2), (1,4), (2,2), (2,4) and (4,4). - _Wesley Ivan Hurt_, May 01 2021
%H A238952 Antti Karttunen, <a href="/A238952/b238952.txt">Table of n, a(n) for n = 1..65537</a>
%H A238952 S.-H. Cha, E. G. DuCasse, and L. V. Quintas, <a href="http://arxiv.org/abs/1405.5283">Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures</a>, arXiv:1405.5283 [math.NT], 2014 (see 13th line in Table 1).
%F A238952 Conjecture: a(n) = Sum_{i=1..floor(n/2)} d(i) * (floor(n/i) - floor((n-1)/i)), where d(n) is the number of divisors of n. - _Wesley Ivan Hurt_, Dec 21 2017
%F A238952 a(n) = Sum_{d|n, d<n} A000005(d). - _Antti Karttunen_, Mar 08 2018, after _Geoffrey Critzer_'s Mathematica-code.
%F A238952 G.f.: Sum_{k>=1} (d(k) - 1)*x^k/(1 - x^k), where d(k) = number of divisors of k (A000005). - _Ilya Gutkovskiy_, Sep 11 2018
%F A238952 a(n) = A007425(n) - A000005(n). - _Ridouane Oudra_, Apr 26 2025
%p A238952 with(numtheory): seq(add(tau(d), d in divisors(n) minus {n}), n=1..80); # _Ridouane Oudra_, Apr 26 2025
%t A238952 Table[Map[DivisorSigma[0, #] &, Drop[Divisors[n], -1]] // Total, {n, 1, 77}] (* _Geoffrey Critzer_, Jan 01 2015 *)
%o A238952 (PARI) A238952(n) = sumdiv(n, d, (d<n)*numdiv(d)); \\ _Antti Karttunen_, Mar 07 2018, after _Geoffrey Critzer_'s Mathematica-code.
%Y A238952 Cf. A000005, A007425, A062799.
%K A238952 nonn
%O A238952 1,4
%A A238952 _Sung-Hyuk Cha_, Mar 07 2014