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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

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If \( p \) and \( q \) are prime numbers, the number of divisors \( d(a) \) of a natural number \( a = p^{\alpha} q^{\beta} \) is given by the formula
$$
d(a) = (\alpha+1)(\beta+1).
$$

For example, \( 12 = 2^2 \times 3^1 \), the number of divisors of 12 is
$$
d(12) = (2+1)(1+1) = 6,
$$

and the divisors are \( 1, 2, 3, 4, 6, \) and \( 12 \).

Using the given calculation formula, answer: Among the divisors of \( 20^{30} \) that are less than \( 20^{15} \), how many are not divisors of \( 20^{15} \)?

Present the answer in LaTex format: \boxed{Your answer}
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