# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a238952 Showing 1-1 of 1 %I A238952 #41 Nov 07 2024 21:59:21 %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, Table of n, a(n) for n = 1..65537 %H A238952 S.-H. Cha, E. G. DuCasse, and L. V. Quintas, Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures, 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=1} (d(k) - 1)*x^k/(1 - x^k), where d(k) = number of divisors of k (A000005). - _Ilya Gutkovskiy_, Sep 11 2018 %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