Those Fascinating Numbers 1 the only number which divides all the others. 2 the only even prime number. 3 the prime number which appears the most often as the second prime factor of an integer, and actually with a frequency of 1 6 (see the number 199 for the list of those prime numbers which appear the most often as the kth prime factor of an integer, for any fixed k 1). the smallest Mersenne prime (3 = 22 −1): a prime number is called a Mersenne prime if it is of the form 2p 1, where p is prime (see the number 131 071 for the list of all Mersenne primes known as of May 2009) the prime number which appears the most often as the second largest prime factor of an integer, that is approximately (1 + log 2 + 3 2 log 3)x/ log x times amongst the positive integers n x (see J.M. De Koninck [44]) the smallest triangular number 1: a number n is said to be triangular if there exists a number k such that n = 1 + 2 + 3 + . . . + k = k(k + 1) 2 . . 1 http://dx.doi.org/10.1090/mbk/064/01
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