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Squarefree Binomial Coefficients

Problem 203

Published on Saturday, 6th September 2008, 02:00 pm; Solved by 5406

The binomial coefficients nCk can be arranged in triangular form, Pascal's triangle, like this:

1
11
121
1331
14641
15101051
1615201561
172135352171
.........

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.