OFFSET
1,12
COMMENTS
Also, number of partitions of n into two distinct parts (s,t), s<t, such that s|n and t|s*n. - Wesley Ivan Hurt, Jan 16 2022
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
FORMULA
a(2n+1) = 0. - Ray Chandler, May 29 2008
a(n) = Sum_{d|n, (d+1)|n, d>1} 1. - Wesley Ivan Hurt, Jan 16 2022
From Amiram Eldar, Dec 31 2023: (Start)
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/2. (End)
EXAMPLE
n=144: divisors(144) = {1,2,3,4,6,8,9,12,16,18,24,36,48,72,144}, there are a(144) = 3 divisors d>1 such that also d+1 divides 144: (2,3), (3,4) and (8,9).
MATHEMATICA
Table[DivisorSum[n, 1 &, And[# > 1, Divisible[n, # + 1]] &], {n, 105}] (* Michael De Vlieger, Jul 12 2017 *)
PROG
(PARI) A088722(n) = sumdiv(n, d, (d>1)&&!(n%(d+1))); \\ Antti Karttunen, Jul 12 2017
(PARI) first(n) = my(v = vector(n), k); for(i=2, sqrtint(n), k=i*(i+1); for(j=1, n\k, v[j*k]++)); v \\ David A. Corneth, Jul 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Oct 12 2003
EXTENSIONS
Extended by Ray Chandler, May 29 2008
STATUS
approved