Anti-Prime
A positive integer is said to be anti-prime if it has more factors than any positive integer less than .
1 has 1 factor ; 2 has 2 factors ; 3 has 2 factors ; 4 has 3 factors ; 5 has 2 factors ; 6 has 4 factors
Thus, the list of anti-primes goes as .
It is a FACT that is an anti-prime with factors, and there is no number below with more than factors.
How many anti-primes are less than ?
Note : Negative numbers are not to be counted towards factors.
The answer is 26.
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1 solution
The list of anti-primes along with their number of factors (in parantheses) are listed below :
1 ( 1 ) , 2 ( 2 ) , 4 ( 3 ) , 6 ( 4 ) , 1 2 ( 6 ) , 2 4 ( 8 ) , 3 6 ( 9 ) , 4 8 ( 1 0 ) , 6 0 ( 1 2 ) , 1 2 0 ( 1 6 ) , 1 8 0 ( 1 8 ) , 2 4 0 ( 2 0 ) , 3 6 0 ( 2 4 ) , 7 2 0 ( 3 0 ) , 8 4 0 ( 3 2 ) , 1 2 6 0 ( 3 6 ) , 1 6 8 0 ( 4 0 ) , 2 5 2 0 ( 4 8 ) , 5 0 4 0 ( 6 0 ) , 7 5 6 0 ( 6 4 ) , 1 0 0 8 0 ( 7 2 ) , 1 5 1 2 0 ( 8 0 ) , 2 0 1 6 0 ( 8 4 ) , 2 5 2 0 0 ( 9 0 ) , 2 7 7 2 0 ( 9 6 ) , 4 5 3 6 0 ( 1 0 0 )