何の

1. pre-noun adjectival, usually in kana which; what (way)

なんの

1. pre-noun adjectival what; what kind of; what sort of
2. with. neg. sentence no ...; any
3. usually in kana, as ...のなんの adds emphasis to the preceding word
4. interjection, usually in kana, used to dismiss someone's concerns, words, etc. no; not at all; oh (it's nothing)