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Burt Kaliski Jr. (@modulomathy)
3/4/12 8:08 PM
#math trivia for #March4: #64 is one of only two sixth powers this year. How many days are nth powers for some n > 1?

Seven days have numbers that are higher powers of 2: 4, 8, 16, 32, 64, 128, 256. There are four higher powers of 3, four higher powers of 4, two of 5, two of 6, and one each of 7 through 19. However, some of these powers are duplicates and should be removed: in particular, anything starting with a number that itself is a higher power, i.e., of 4, 8, 9, or 16. The remaining numbers thus include:

• seven powers of 2
• four powers of 3
• two powers of 5
• two powers of 6
• one each of 7, 10, 11, 12, 13, 14, 15, 17, 18, 19

The total number of days that are higher powers is 25.