think up vs think of

think up and think of both are verbs.

Word	Noun	Adjective	Verb	Adverb
think up	No	No	Yes	No
think of	No	No	Yes	No

As verbs, think up and think of are synonyms defined as:

Other synonyms of think up include concoct, dream up, hatch.

think up (verb)	think of (verb)
devise or invent	keep in mind for attention or consideration
	look on as or consider
	intend to refer to
	take into consideration, have in view
	choose in one's mind
	devise or invent