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

Author

Omar E. Pol, Apr 07 2018

Keywords

• nonn

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)).

Examples

			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.
		

Crossrefs

Cf. A000203, A067742, A067743, A071090.

Programs

Mathematica

Table[DivisorSum[n, # &, Or[#^2 < n/2, #^2 >= 2 n] &], {n, 75}] (* Michael De Vlieger, Apr 21 2018 *)

PARI

a(n) = sumdiv( n, d, d*(d*d= 2*n)); \\ Michel Marcus, Apr 20 2018

Formula

a(n) = A000203(n) - A071090(n).