A299777 a(n) is the sum of middle divisors of the n-th number that has middle divisors.

1, 1, 2, 5, 2, 3, 7, 8, 4, 3, 9, 10, 5, 11, 11, 4, 12, 6, 13, 13, 14, 14, 7, 5, 15, 15, 16, 16, 8, 17, 17, 23, 18, 18, 9, 19, 19, 19, 20, 20, 7, 20, 10, 21, 21, 21, 22, 22, 45, 11, 23, 23, 23, 24, 24, 24, 37, 25, 26, 25, 25, 26, 26, 26, 13, 27, 27, 55, 27, 28, 29, 28, 28, 14, 29, 10, 29, 29, 30, 29

Offset: 1

Author

Omar E. Pol, Apr 07 2018

Keywords

• nonn

Comments

The middle divisors of n, are the divisors in the half-open interval [sqrt(n/2), sqrt(n*2)).

Examples

			For n = 12 the 12th number that has middle divisors is 24. The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The middle divisors of 24 are 4 and 6, and the sum of them is 4 + 6 = 10, so a(12) = 10.
		

Crossrefs

Nonzero terms in A071090.

Companion of A281007.

Cf. A071562.

Programs

PARI

lista(nn) = for (n=1, nn, if (s=sumdiv(n, d, if(d^2>=n/2 && d^2<2*n, d, 0)), print1(s, ", "))); \\ Michel Marcus, Apr 24 2018

Formula

a(n) = A071090(A071562(n)).