162

162 = 2 x 3⁴.

162 is the only number with a prime factorization of the form n * (n + 1)⁽ⁿⁿ⁾.

162 has a representation as a sum of two squares: 162 = 9² + 9².

162 is the smallest number with nine representations as a sum of four positive squares: 162 = 1² + 1² + 4² + 12² = 1² + 2² + 6² + 11² = 1² + 4² + 8² + 9² = 1² + 5² + 6² + 10² = 2² + 3² + 7² + 10² = 3² + 4² + 4² + 11² = 3² + 5² + 8² + 8² = 3² + 6² + 6² + 9² = 4² + 4² + 7² + 9².

162 is a divisor of 55³ - 1.

162 is an abundant number.

The digit sum of 162 is 9; the digit sum of the square of 162 is 18, and the digit sum of the cube of 162 is 27.

162 is the total number of baseball games each team plays during a regular season of Major League Baseball.

Source: Prime Curios!

945

945 = 3³ x 5 x 7.

945 is the first odd abundant number, discovered by Claude-Gaspar Bachet (1581-1638): 945 = 3³ x 5 x 7 and its divisors sum to 975; 975 is greater than 945, so 945 is an abundant number. Odd abundant number are rare; only 23 occur below 10,000.

945 is the smallest odd primitive semiperfect number. A semiperfect number is equal to the sum of all or some of its proper divisors. A semiperfect number that is not divisible by any smaller semiperfect number is a primitive semiperfect number.

945 is 1661 in base 8.


NGC 945 is a galaxy in the constellation Cetus.

Source: Wolfram MathWorld