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# Index entries for number of divisors

A000005 gives the number of divisors $n\,$ (see also divisor function).

The following table lists sequences defined by numbers having a specific number of divisors.

Numbers with a given number of divisors
A-number $\tau \,$ Description
1 The unit 1
A000040 2 Prime numbers
A001248 3 Squares of primes
A030513 4 Squarefree semiprimes and cubes of primes
A030514 5 Fourth powers of primes
A030515 6 Fifth powers of primes are a subset
A030516 7 Sixth powers of primes
A030626 8 Sphenic numbers are a subset
A030627 9 Eighth powers of primes are a subset
A030628 10
A030629 11 Tenth powers of primes
A030630 12
A030631 13 Twelfth powers of primes
A030632 14
A030633 15
A030634 16
A030635 17 Sixteenth powers of primes
A030636 18
A030637 19 Eighteenth powers of primes
A030638 20
A137484 21
A137485 22
A137486 23 Twenty-second powers of primes
A137487 24
A137488 25
A137489 26
A137490 27
A137491 28
A137492 29 Twenty-eighth powers of primes
A137493 30
A139571 31 Thirtieth powers of primes
A175742 32
A175743 33
A175744 34
A175745 35
A175746 36
A139572 37 Thirty-sixth powers of primes
A175747 38
A175748 39
A175749 40
A139573 41 Fortieth powers of primes
A175750 42
A139574 43 Forty-second powers of primes
A175751 44
A175752 45
A175753 46
A139575 47 Forty-sixth powers of primes
A175754 48
A175755 49
A175756 50
51
52
A173533 53 Fifty-second powers of primes