A355143 Product of middle divisors of n, or 0 if there are no middle divisors of n.

1, 1, 0, 2, 0, 6, 0, 2, 3, 0, 0, 12, 0, 0, 15, 4, 0, 3, 0, 20, 0, 0, 0, 24, 5, 0, 0, 28, 0, 30, 0, 4, 0, 0, 35, 6, 0, 0, 0, 40, 0, 42, 0, 0, 45, 0, 0, 48, 7, 5, 0, 0, 0, 54, 0, 56, 0, 0, 0, 60, 0, 0, 63, 8, 0, 66, 0, 0, 0, 70, 0, 432, 0, 0, 0, 0, 77, 0, 0, 80

Offset

1,4

Links

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

Example

For n = 6 the middle divisors of 6 are 2 and 3, the product of them is 2*3 = 6, so a(6) = 6.
For n = 7 there are no middle divisors of 7, so a(7) = 0.
For n = 8 there is only one middle divisor of 8, the 2, so a(8) = 2.
For n = 72 the middle divisors of 72 are [6, 8, 9], the product of them is 6*8*9 = 432, so a(72) = 432.

Mathematica

a[n_] := If[(p = Product[If[Sqrt[n/2] <= d < Sqrt[2*n], d, 1], {d, Divisors[n]}]) == 1 && n > 2, 0, p]; Array[a, 100] (* Amiram Eldar, Jun 21 2022 *)

Prog

(PARI) a(n) = my(v=select(x->((x >= sqrt(n/2)) && (x < sqrt(n*2))), divisors(n))); if (#v, vecprod(v), 0); \\ Michel Marcus, Aug 04 2022

Crossrefs

Row products of A299761.

Indices of zeros give A071561.

Indices of nonzeros give A071562.

Cf. A007955, A067742, A071090, A320142, A347950.

Sequence in context: A262886 A138701 A332400 * A274878 A050821 A076257

Adjacent sequences: A355140 A355141 A355142 * A355144 A355145 A355146

Keyword

nonn

Author

Omar E. Pol, Jun 20 2022

Extensions

More terms from Amiram Eldar, Jun 21 2022

Status

approved