A302433 a(n) is the sum of the nonmiddle divisors of n.

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)).

Links

Table of n, a(n) for n=1..75.

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

Cf. A000203, A067742, A067743, A071090.

Sequence in context: A091871 A303393 A039085 * A326749 A327111 A326853

Adjacent sequences: A302430 A302431 A302432 * A302434 A302435 A302436

Keyword

nonn

Author

Omar E. Pol, Apr 07 2018

Status

approved