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A302433
a(n) is the sum of the nonmiddle divisors of n.
4
0, 2, 4, 5, 6, 7, 8, 13, 10, 18, 12, 21, 14, 24, 16, 27, 18, 36, 20, 33, 32, 36, 24, 50, 26, 42, 40, 45, 30, 61, 32, 59, 48, 54, 36, 85, 38, 60, 56, 77, 42, 83, 44, 84, 64, 72, 48, 110, 50, 88, 72, 98, 54, 105, 72, 105, 80, 90, 60, 152, 62, 96, 88, 119, 84, 127, 68, 126, 96, 127, 72, 172, 74, 114, 124
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)).
FORMULA
a(n) = A000203(n) - A071090(n).
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