69 (number) - Wikipedia

69 is a semiprime, or a natural number that is the product of exactly two prime numbers (3 and 23). It is an interprime, sitting between 67 and 71.[1][2] 69 is not divisible by any square number other than 1, making it a square-free integer.[3] 69 is a Blum integer since the two factors of 69 are both Gaussian primes, and an Ulam number, an integer that is the sum of two distinct previously occurring Ulam numbers in a sequence.[a][4][6] 69 is a deficient number because the sum of its proper divisors (which excludes itself) is less than itself.[7] As an integer for which the arithmetic mean average of its positive divisors is also an integer, 69 is an arithmetic number.[8] 69 is a congruent number—a positive integer that is the area of a right triangle with three rational number sides—and an amenable number.[9][10] 69 can be expressed as the sum of consecutive positive integers in multiple ways, making it a polite number.[11] 69 is a lucky number because it is a natural number that remains after repeatedly removing every nth number in a sequence of natural numbers, starting from 1.[b][13][14]

In decimal, 69 is the only natural number whose square (4761) and cube (328509) use every digit from 0–9 exactly once.[15][16] It is also the largest number whose factorial is less than a googol. On many handheld scientific and graphing calculators, 69! (1.711224524×1098) is the highest factorial that can be calculated due to memory limitations.[17] In its binary expansion of 1000101,[18] 69 is equal to 105 octal, while 105 is equal to 69 hexadecimal (this same property can be applied to all numbers from 64 to 69).[19][20] In computing, 69 equates to 2120 in ternary (base-3); 153 in senary (base-6); and 59 in duodecimal (base-12).[21][22][23]

Visually, in Arabic numerals, 69 is a strobogrammatic number because it looks the same when viewed both right-side and upside down.[24] 69 is a centered tetrahedral number, a figurate number that represents a pyramid with a triangular base and all other points arranged in layers above the base, forming a tetrahedron shape.[25] 69 is also a pernicious number because there is a prime number of 1s when it is written as a binary number, and an odious number, as it is a positive integer that has an odd number of 1s in its binary expansion.[26][27]