What picture control do you have set on the D3400? If you shoot in raw, you will either have to use Nikon's own software in post to make use of the Picture controls or use Adobe's approximations in Lightroom. Both [LS] Landscape and [VI] Vivid have higher colour saturation than [SD] Standard. If you prefer .jpg, this setting is baked into the file.
As long as you don't shoot directly toward the sun, a polarizing filter will help in capturing these vivid colours in nature.
I suppose the point-and-shoot had some kind of vivid colour enhancing algorithm baked into the settings for landscape photography.
The editing exercises for the last three weeks have been mostly about manipulating the sky to enhance a rather dull rendering straight out of camera. It might be worth taking a look.
Editing exercise, week ending Jan. 15 2017 - Mini-Challenges, Member Contests, and Games - NikonForums.com
Editing exercise, week ending Jan. 22 2017 - Mini-Challenges, Member Contests, and Games - NikonForums.com
Editing exercise, week ending Jan. 29 2017 - Mini-Challenges, Member Contests, and Games - NikonForums.com