Basic Examples (2) 

Show that 54 is 7-smooth:

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54 is not 2-smooth, since its prime factors are 2 and 3:

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Scope (2) 

The following is an operator which tests whether an integer is 7-smooth:

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An integer is p-smooth for non-prime p if it is p-smooth for p being the greatest prime less than p:

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π - smooth numbers are the same as 3-smooth numbers:

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Applications (1) 

Print the 7-smooth numbers less than or equal to 100:

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Properties and Relations (3) 

A negative integer is considered smooth if its absolute value is smooth:

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Test that if n is 5-smooth, then so is -n for n up to 100:

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Any input besides an integer in the first argument gives False:

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Negative values for the second input always return False:

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Neat Examples (2) 

Calculate the number of "humble numbers" (7-smooth integers) with 1, 2, 3, 4 and 5 digits:

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123200 and 123201 comprise the largest consecutive pair that are both 13-smooth:

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