GOTW- Counting - Page 5

Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways: 50 = 1² + 7² = 5² + 5².^[1] It is also the sum of three squares, 50 = 3² + 4² + 5². It is a Harshad number.

There is no solution to the equation f(x) = 50, making 50 a nontotient. Nor is there a solution to the equation x - f(x) = 50, making 50 a noncototient.

The aliquot sum of 50 is 43 and its aliquot sequence is (50,43,1,0). Fifty is itself the aliquot sum of 40 and 94.

Fifty-one is the 14th discrete biprime and the 5th in the {3.q} semiprime family having the prime factors (3.17). The aliquot sum of 51 is 21, itself a discrete biprime. 51 is the 4th member of the 11-aliquot tree with the sequence (51, 21, 11, 1, 0).

51 is a pentagonal number as well as a centered pentagonal number (one of the few numbers to be both) and an 18-gonal number and a Perrin number. It is also the 6th Motzkin number, telling the number of ways to draw non-intersecting chords between any six points on a circle's boundary, no matter where the points may be located on the boundary.

Since the greatest prime factor of 51² + 1 = 2602 is 1301, which is clearly more than 51 twice, 51 is a Strmer number.

Originally posted by: sheila1990

Whats a Harshad number lol