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

1,3

Comments

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

Links

Table of n, a(n) for n=1..80.

Formula

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

Example

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.

Prog

(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

Crossrefs

Nonzero terms in A071090.

Companion of A281007.

Cf. A071562.

Sequence in context: A087892 A078372 A154751 * A197545 A187017 A083381

Adjacent sequences: A299774 A299775 A299776 * A299778 A299779 A299780

Keyword

nonn

Author

Omar E. Pol, Apr 07 2018

Status

approved