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A299777
a(n) is the sum of middle divisors of the n-th number that has middle divisors.
13
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)).
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 07 2018
STATUS
approved