Insert multiple rows of default values into a table

I have a table with a single column, which is an auto-generated identity

create table SingleIdTable (
   id int identity(1,1) not null
)

I can insert a single row with an auto-generated id with:

insert into SingleIdTable default values

I want to insert many rows and use the output syntax to get their ids, something like:

insert into SingleIdTable
output inserted.Id into @TableOfIds
    select (default values) from SomeOtherTable where Attribute is null

Where the intention is to insert a row into SingleIdTable for each row in SomeOtherTable where Attribute is null using an auto-generated id. The above doesn't work, but how could I do it. I note that if my table had more than just a single column I could do it, but I can't select empty rows which is what I really want to do.

I can't change the definition of SomeOtherTable.