| Highly Totient Number |
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1 , 2 , 4 , 8 , 12 , 24 , 48 , 72 , 144 , 240, 432 , 480, 576, 720 , 1152, 1440 . with 1, 3, 4, 5, 6, 10, 11, 17, 21, 31, 34, 37, 38, 49, 54, and 72 totient solutions respectively. The sequence of highly totient numbers is a subset of the sequence of smallest number ''k'' with exactly ''n'' solutions to φ(''x'') = ''k''. The concept is somewhat analogous to that of Highly Composite Number s, and in the same way that 1 is the only odd highly composite number, it is also the only odd highly totient number (indeed, the only odd number to not be a Nontotient ). And just as there are infinitely many highly composite numbers, there are also infinitely many highly totient numbers, though the highly totient numbers get tougher to find the higher one goes, since calculating the totient function involves factorization into Prime s, something that becomes extremely difficult as the numbers get larger. See also Highly Cototient Number . |
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