# Category:Tau Function

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This category contains results about the divisor counting function $\tau$ (tau function).

Let $n$ be an integer such that $n \ge 1$.

The **divisor counting function** is defined on $n$ as being the total number of positive integer divisors of $n$.

It is denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ as $\tau$ (the Greek letter **tau**).

That is:

- $\displaystyle \map \tau n = \sum_{d \mathop \divides n} 1$

where $\displaystyle \sum_{d \mathop \divides n}$ is the sum over all divisors of $n$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### N

### P

### T

## Pages in category "Tau Function"

The following 170 pages are in this category, out of 170 total.

### D

- Divisor Counting Function is Primitive Recursive
- Divisor Counting Function/Examples
- Divisor Counting Function/Examples/1
- Divisor Counting Function/Examples/105
- Divisor Counting Function/Examples/108
- Divisor Counting Function/Examples/110
- Divisor Counting Function/Examples/12
- Divisor Counting Function/Examples/120
- Divisor Counting Function/Examples/3
- Divisor Counting Function/Examples/60
- Divisor Counting Function/Table

### I

### N

### P

### S

- Sequence of 4 Consecutive Integers with Equal Number of Divisors
- Sequence of 9 Consecutive Integers each with 48 Divisors
- Sequence of Consecutive Integers with Same Number of Divisors
- Smallest Consecutive Even Numbers such that Added to Divisor Count are Equal
- Smallest Number with 16 Divisors
- Smallest Number with 2^n Divisors
- Smallest Numbers with 240 Divisors
- Smallest Triplet of Integers whose Product with Tau Value are Equal

### T

- Tau Function from Prime Decomposition
- Tau Function is Multiplicative
- Tau Function Odd Iff Argument is Square
- Tau Function of 1
- Tau Function of 104
- Tau Function of 105
- Tau Function of 108
- Tau Function of 110
- Tau Function of 111,111
- Tau Function of 116
- Tau Function of 117
- Tau Function of 1184
- Tau Function of 1190
- Tau Function of 12
- Tau Function of 120
- Tau Function of 1260
- Tau Function of 1312
- Tau Function of 1330
- Tau Function of 1376
- Tau Function of 14
- Tau Function of 140
- Tau Function of 1430
- Tau Function of 147
- Tau Function of 148
- Tau Function of 15
- Tau Function of 1575
- Tau Function of 1638
- Tau Function of 168
- Tau Function of 1680
- Tau Function of 17,796,126,877,482,329,126,043
- Tau Function of 17,796,126,877,482,329,126,044
- Tau Function of 17,796,126,877,482,329,126,045
- Tau Function of 17,796,126,877,482,329,126,046
- Tau Function of 17,796,126,877,482,329,126,047
- Tau Function of 17,796,126,877,482,329,126,048
- Tau Function of 17,796,126,877,482,329,126,049
- Tau Function of 17,796,126,877,482,329,126,050
- Tau Function of 17,796,126,877,482,329,126,051
- Tau Function of 17,796,126,877,482,329,126,052
- Tau Function of 17,796,126,877,482,329,126,053
- Tau Function of 171
- Tau Function of 172
- Tau Function of 18
- Tau Function of 180
- Tau Function of 190
- Tau Function of 192
- Tau Function of 2
- Tau Function of 20
- Tau Function of 21,952
- Tau Function of 210
- Tau Function of 2205
- Tau Function of 224
- Tau Function of 24
- Tau Function of 240
- Tau Function of 242
- Tau Function of 243
- Tau Function of 244
- Tau Function of 245
- Tau Function of 248
- Tau Function of 2520
- Tau Function of 264
- Tau Function of 27
- Tau Function of 270
- Tau Function of 272
- Tau Function of 28
- Tau Function of 3
- Tau Function of 30
- Tau Function of 304
- Tau Function of 32
- Tau Function of 332
- Tau Function of 333
- Tau Function of 35
- Tau Function of 350
- Tau Function of 357
- Tau Function of 360
- Tau Function of 3600
- Tau Function of 3655
- Tau Function of 3656
- Tau Function of 3657
- Tau Function of 3658
- Tau Function of 368
- Tau Function of 4,100,625
- Tau Function of 40,310
- Tau Function of 40,311
- Tau Function of 40,312
- Tau Function of 40,313
- Tau Function of 40,314
- Tau Function of 40,315
- Tau Function of 40,316
- Tau Function of 4030
- Tau Function of 42
- Tau Function of 420
- Tau Function of 44
- Tau Function of 45
- Tau Function of 464
- Tau Function of 490
- Tau Function of 496
- Tau Function of 5040
- Tau Function of 52
- Tau Function of 550
- Tau Function of 56
- Tau Function of 570
- Tau Function of 572
- Tau Function of 6
- Tau Function of 60
- Tau Function of 616
- Tau Function of 625
- Tau Function of 630
- Tau Function of 64
- Tau Function of 64,000
- Tau Function of 650
- Tau Function of 6561
- Tau Function of 672
- Tau Function of 70
- Tau Function of 720
- Tau Function of 720,720
- Tau Function of 748
- Tau Function of 75
- Tau Function of 7560
- Tau Function of 76
- Tau Function of 770
- Tau Function of 78
- Tau Function of 8128
- Tau Function of 830,600
- Tau Function of 831,600
- Tau Function of 836
- Tau Function of 840
- Tau Function of 88
- Tau Function of 90
- Tau Function of 910
- Tau Function of 9240
- Tau Function of 942,480
- Tau Function of 945
- Tau Function of 98
- Tau Function of 982,800
- Tau Function of 99
- Tau Function of 997,920
- Tau Function of Square-Free Integer is Power of 2
- Tau of Power of Prime
- Tau of Prime Number