4511.sagews

@interact
def find_factors(n=(1..30)):
    data = [[var("k"), "$2+k$", "$(n+1)!/(2+k)$", "product", "factorization"]]
    for k in srange(n):
        a, b = 2+k, factorial(n+1)/(2+k) + 1
        product = a * b
        data.append([k, a, b, product, factor(product)])
    html.table(data, True)