Number of renown and infamy, I am an odd multiple of three. Change my orientation and I may stay the same. Each time I'm referenced, the responses do not change.

This particular number holds a unique place in popular culture and mathematics, making it a clever answer to the riddle. It is indeed an odd multiple of three, as 69 divided by three equals 23, and 69 is not an even number. Its "renown and infamy" stem from its well-known suggestive connotation, which has made it a recurring motif in humor and popular media.

One of the most intriguing aspects of this number, and a key to the riddle, is its visual property. If you rotate the digits 6 and 9 by 180 degrees, they simply swap positions, resulting in the number 69 appearing the same. This characteristic makes it a type of strobogrammatic number, though the term itself is not needed to appreciate the visual trick. This rotational symmetry adds a layer of cleverness to its identity.

The final clue refers to a widespread internet phenomenon. Whenever this specific number is mentioned online, it almost invariably elicits the same simple, one-word response: "nice." This consistent reaction has become an established meme, further solidifying the number's unique cultural footprint and making its reference instantly recognizable to many. This blend of mathematical properties, visual quirks, and cultural significance makes it a truly memorable number.