In January, Mr. Purzycki tapped a number of large influencers who he had formed relationships with through his association with Jerry Media. (Elliot Tebele, the founder of Jerry Media, has no involvement in the project.)

The campaign, which began this week, has already placed sponsored posts on Instagram accounts including @GrapeJuiceBoys, a meme page with more than 2.7 million followers; Jerry Media’s own most popular account, with more than 13.3 million followers; and @Tank.Sinatra, a member with more than 2.3 million followers.

The accounts all posted Bloomberg campaign ads in the form of fake direct messages from the candidate.