Prime Curios!: 153

153
(another Prime Pages' Curiosity)

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153 is equal to the alternating sum and difference of the squares of the integers from 1 to 153's largest prime factor, 17. [Cramer]

(153) = (15) x 3!. [Gupta]

153 is the sum of all the integers from 1 to 17 (which is prime).

2^2 * 7 + 5^3 = 1*1*1 + 5*5*5 + 3*3*3 = (1+5+3) * 17 = 1! + 2! + 3! + 4! + 5! = N. Note: (a) representation with first four primes only, (b1) sum of first three odd cubes and bases are digits of N, divisible by three primes (counted with multiplicity), (b2) Harshad-Niven-Kaprekar number, i.e., divisible by the sum of its digits, (c) sum of first five faculties. [Zschorn]