= 47-smooth number
= 47-smooth
{synonym}
A <47-smooth number> is a positive <integer> whose <prime factors> are all at most $47$. Equivalently, it is a product of nonnegative powers of $2,3,5,7,11,13,17,19,23,29,31,37,41,43,47$. The number one is included as the empty product.
For example, $47\cdot2^{10}$ is <47-smooth>, while $53$ is not. The bound constrains the <prime factors> rather than the size of the number. Such classes make multiplicative searches manageable by replacing an arbitrary factorization with an <exponent vector> over a fixed finite prime set.
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