Weight isn't the only factor. Washer vibration during spin is a concern if the floor isn't structurally reinforced to handle the forces.

I would suggest you build a platform to distribute the weight and mitigate any vibration before it get to the floor.

I also suggest a floor drain just in case of an overflow, you don't want the bdrm below flooded.

To do this properly, build the platform as a shallow box. Waterproof the top of the box and up the sides minimum of 4" with Kherdi cloth and tile, Put the floor drain where it can be reached without moving the washer.

I think your plan will be pushing things too far; my 40/10 span table doesn't get up to 13' spans, and a 400# point load is a substantial load to deal with! Since this is an attic, I would assume the ceiling joists for the room below could be readily exposed. If it were me, I would over-build the supporting structure; the stiffer the ceiling joist structure below is, the less issue you will have with vibration. As a minimum I would sister 2x8's to each existing ceiling joist below using construction glue and screws, install blocking between joists and then glue and screw down 3/4" AdvanTech as the laundry room floor. The drain pan leading to a drain as stated above is a must. Also, it's a bit pricey, but being on the 3rd floor of a house, I would install an automatic water leak shutoff control like this or similar:

https://www.amazon.com/Watts-A2C-SC-WB-intelliflow-shutoff-valve/dp/B0937G9972/ref=sr_1_1_sspa?hvadid=324337686445&hvdev=c&hvlocphy=9016116&hvnetw=g&hvqmt=e&hvrand=11118298106564948765&hvtargid=kwd-326900264062&hydadcr=12694_9717487&keywords=watts%2Bautomatic%2Bshut%2Boff%2Bvalve&qid=1701798559&sr=8-1-spons&sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1

It is not obvious to me why you would want a washer there?…

@Stax, what's OP?

OP is original poster.