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A355143 Product of middle divisors of n, or 0 if there are no middle divisors of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 29 13:51 EST 2023. Contains 359923 sequences. (Running on oeis4.)