Index entries for number of divisors

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A000005 gives the number of divisors $\scriptstyle n\,$ (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
N/A	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
	54
	55
	56
	57
	58
A183062	59	Fifty-eighth powers of primes
	60
A183085	61	Sixty powers of primes
	62
	63
	64
	65
	66
A280298	67	Fifty-sixth powers of primes
	68
	69
	70
A280299	71	Seventy powers of primes
	72
A280301	73	Seventy-second powers of primes
	74
	75
	76
	77
	78
A280346	79	Seventy-eighth powers of primes
	80
	81
	82
A280347	83	Eighty-second powers of primes
	84
	85
	86
	87
	88
A280349	89	Eighty-eighth powers of primes
	90
	91
	92
	93
	94
	95
	96
A280350	97	Ninety-sixth powers of primes
	98
	99
	100
A261700	101	One hundred powers of primes