A343281 Numbers of the form x + y + z in positive integers x,y,z such that (x+y) | x*y, (y+z) | y*z, and (x+z) | x*z.

6, 12, 15, 18, 20, 24, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 66, 70, 72, 75, 77, 78, 80, 84, 88, 90, 91, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, 140, 143, 144, 150, 153, 154, 156, 160, 162, 165, 168, 170, 174, 175, 176, 180, 182, 184

Offset

1,1

Comments

Not the same as A005279, this sequence contains 184.

Links

Table of n, a(n) for n=1..64.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} c(i*j/(i+j)) * c(i*(n-i-j)/(n-j)) * c(j*(n-i-j)/(n-i)), where c(n) = 1 - ceiling(n) + floor(n).

Example

184 = [120,40,24] so that (120+40) | 120*40, (40+24) | 40*24, (120+24) | 120*24.

Crossrefs

Cf. A005279.

Sequence in context: A107487 A092671 A005279 * A375611 A129512 A259366

Adjacent sequences: A343278 A343279 A343280 * A343282 A343283 A343284

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 10 2021

Status

approved