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That would depend on what you mean by "ok." Assuming you get the lens with a Nikon mount, it will fit onto the D40 and meter properly. However, the D40 lacks an autofocus motor and thus this lens will not autofocus. You can still focus manually.
If those lenses have a Nikon mount then they will fit on the D3000 and D3100. However, the D3000 and D3100 lack a focus motor. If the lens does not have the focus motor then you will not have the autofocus capability. Sigma calls their focus motor the HSM; if the lens does not specify HSM then they do not have the motor.
All after market lenses are specifically designed for a brand of camera. They are for Nikon, Cannon, Minolta etc.. They can not be cross branded just as you could not use a Nikon made lens on a Pentax.
The Sigma 70-300mm f/4-5.6 DG will not autofocus with the D40 since the lens does not feature an internal focusing motor (HSM). The D40 does not have an AF motor in the body and hence it can autofocus only with lenses featuring an integrated motor (eg. Nikon AF-S lenses, Sigma HSM lenses, Tokina DX II series etc). Unfortunately you can use the said lens only in MF mode.
Unfortunately, this lens is not supported by the D40 due to Nikon's unfortunate decision to leave out the autofocus motor from this camera. This is why I tell folks not to waste their money on the D40 - access to the many, many, many lenses that Nikon has made over the years, many of which are available used for a substantial savings, is lost on this camera. The only Nikon lenses that work are AF-S lenses, and some third party lenses that have their own internal motors. I got a list of Sigma lenses that are compatible with the D40 for you:
The list of compatible Sigma lenses for the Nikon D40 as of the current date is as follows:
10-20mm F4-5.6 EX DC
17-35mm F2.8-4 DG
50-500mm F4-6.3 DG
APO 50-150mm F2.8 EX DC HSM
70-200mm F2.8 DG MACRO
100-300mm F4 DG
120-300mm F2.8 DG
300-800mm F5.6 DG
14mm F2.8 EX
30mm F1.4 EX DC HSM
150mm F2.8 EX DG
180mm F3.5 EX DG
300mm EX DG
500mm EX DG
800mm f5.6 EX DG
from here: http://www.imaging-resource.com/NEWS/1177682545.html Sorry for the bad news. The cheaper thing at this point may be to sell the D40 and get a D80. I personally have a D70S, but that is no longer made.