何となく

Compound of 何 (nan, “what”, combining form of nani) +‎ と (to, adverbial particle) +‎ なく (naku, adverbial form of ない nai, “not; without”).^[1]

何と (nan to) is used to mean "somehow, somewhat, kinda":

この間(あいだ)は何(なん)と寒(さむ)いね。

Kono aida wa nan to samui ne.

It's been kinda cold this while, hasn't it.

The addition of the なく (naku) on the end serves to emphasize the vagueness: somehow or other, kinda sorta.

• (Tokyo) なんとなく [nàńtónáꜜkù] (Nakadaka – [4])^[1]
• IPA^(key): [nã̠nto̞na̠kɯ̟]

何(なん)となく • (nantonaku) 

1. somehow or other,  for some reason or another
2. somewhat, to some degree