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5.5 Superfactorials (alternative definition)

Clifford Pickover in his 1995 book Keys to Infinity defined the superfactorial of n, written as n$ (the $ should really be a factorial sign ! with an S superimposed) as

where the ⁽⁴⁾ notation denotes the hyper4 operator, or using Knuth's up-arrow notation,

This sequence of superfactorials starts:

6 Prime factorization of factorials

The power of p occurring in the prime factorization of n! is

This formula allows large factorials to be factored efficiently.

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