Squarefree Binomial Coefficients
September 06, 2008
The binomial coefficients nCk can be arranged in triangular form, Pascal's triangle, like this:
| 1 | ||||||||||||||
| 1 | 1 | |||||||||||||
| 1 | 2 | 1 | ||||||||||||
| 1 | 3 | 3 | 1 | |||||||||||
| 1 | 4 | 6 | 4 | 1 | ||||||||||
| 1 | 5 | 10 | 10 | 5 | 1 | |||||||||
| 1 | 6 | 15 | 20 | 15 | 6 | 1 | ||||||||
| 1 | 7 | 21 | 35 | 35 | 21 | 7 | 1 | |||||||
It can be seen that the first eight rows of Pascal's triangle contain twelve distinct numbers: 1, 2, 3, 4, 5, 6, 7, 10, 15, 20, 21 and 35.
A positive integer n is called squarefree if no square of a prime divides n. Of the twelve distinct numbers in the first eight rows of Pascal's triangle, all except 4 and 20 are squarefree. The sum of the distinct squarefree numbers in the first eight rows is 105.
Find the sum of the distinct squarefree numbers in the first 51 rows of Pascal's triangle.
Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter