OFFSET
1,4
COMMENTS
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
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
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
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).
FORMULA
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
a(n) = Sum_{d|n, d<n} A000005(d). - Antti Karttunen, Mar 08 2018, after Geoffrey Critzer's Mathematica-code.
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
MATHEMATICA
Table[Map[DivisorSigma[0, #] &, Drop[Divisors[n], -1]] // Total, {n, 1, 77}] (* Geoffrey Critzer, Jan 01 2015 *)
PROG
(PARI) A238952(n) = sumdiv(n, d, (d<n)*numdiv(d)); \\ Antti Karttunen, Mar 07 2018, after Geoffrey Critzer's Mathematica-code.
CROSSREFS
KEYWORD
nonn
AUTHOR
Sung-Hyuk Cha, Mar 07 2014
STATUS
approved