I would tell them that you've applied for [whatever], that you've given their names as references, and that they should be expecting a call from [whomever]. That's considered courteous -- and it's advantageous (to you) for your references to be on notice that they may be contacted. Whether it's annoying is up to them. It shouldn't be...
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Put the curse of loneliness on every boy and every girl,
Until everybody's kickin', everybody's scratchin',
Everything seems to fail ?
And it was all for the want of a nail.