A133947 a(n) = the number of "non-isolated divisors" of n(n+1). A positive divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.

2, 3, 4, 4, 5, 5, 4, 6, 7, 4, 6, 6, 4, 8, 8, 4, 5, 5, 6, 11, 7, 4, 6, 8, 4, 5, 8, 4, 7, 7, 4, 8, 5, 4, 15, 6, 4, 5, 10, 6, 7, 7, 4, 12, 9, 4, 6, 9, 4, 7, 8, 4, 5, 10, 10, 9, 5, 4, 8, 8, 4, 7, 10, 6, 9, 5, 4, 6, 10, 4, 8, 8, 4, 7, 10, 4, 11, 5, 6, 13, 5, 4, 8, 15, 4, 5, 8, 4, 9, 13, 6, 6, 5, 4, 12, 6, 4, 9