Burt Kaliski Jr. (@modulomathy)

4/24/12 6:54 PM

#math trivia for #April24: #115 is 5*23; digit-sum of each prime factor is the same. What other day-numbers this year does this happen?

The other possibilities are, by digit-sum,

— 2: 4, 22, 202

— 3: 9

— 4: 169

— 5: 25, 115, 205

— 6: none

— 7: 49, 301

— 8: 289

— 9: none

— 10: 361

Here, I’ve limited to numbers with two prime factors, which may be the same. One of the prime factors must be less than 20, so the largest possible digit-sum is 10. If numbers with just one prime factor were allowed, then all of the primes up to 366 would also be included. If numbers with three or more prime factors were also included, there would be many other possibilities including all prime powers and other numbers where one of the factors above is repeated:

— 2: 4, 8, 16, 32, 64, 128, 256; 44, 88, 176; 242

— 3: 27, 81, 243

— 5: 125

— 7: 343

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