OFFSET
1,2
COMMENTS
The nonmiddle divisors of n are here the divisors of n that are not in the half-open interval [sqrt(n/2), sqrt(n*2)).
EXAMPLE
For n = 12 the divisors of 12 are [1, 2, 3, 4, 6, 12] and the middle divisors of 12 are [3, 4]. The divisors of 12 that are not middle divisors are called here the "nonmiddle" divisors of 12; they are [1, 2, 6, 12] and the sum of them is 1 + 2 + 6 + 12 = 21, so a(12) = 21.
MATHEMATICA
Table[DivisorSum[n, # &, Or[#^2 < n/2, #^2 >= 2 n] &], {n, 75}] (* Michael De Vlieger, Apr 21 2018 *)
PROG
(PARI) a(n) = sumdiv( n, d, d*(d*d<n/2 || d*d >= 2*n)); \\ Michel Marcus, Apr 20 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 07 2018
STATUS
approved