The Rules and Equations Associated with the Phi Function
The Phi is described as the number of positive integers less than n
(positive integer) which have no factor, other than 1, in common,
co-prime, with n.
In my investigation I aim to identify and explain the rules and
equations associated with the Phi function. To go about this I will
investigate Φ (n). This will be further touched upon and will help me
investigate and support any conclusions I hope to gain from
investigating whether (a x b) = (a) x (b) in certain cases.
Table of PhiÂ’s from 2-40
Number
Phi
Φ2
1,
1
Φ3
1,2
2
Φ4
1,2,3
2
Φ5
1,2,3,4
4
Φ6
1,2,3,4,5
2
Φ7
1,2,3,4,5,6
6
Φ8
1,2,3,4,5,6,7
4
Φ9
1,2,3,4,5,6,7,8
6
Φ10
1,2,3,4,5,6,7,8,9
4
Φ11
1,2,3,4,5,6,7,8,9,10
10
Φ12
1,2,3,4,5,6,7,8,9,10,11
4
Φ13
1,2,3,4,5,6,7,8,9,10,11,12
12
Φ14
1,2,3,4,5,6,7,8,9,10,11,12,13
6
Φ15
1,2,3,4,5,6,7,8,9,10,11,12,13,14
8
Φ16
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
8
Φ17
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
16
Φ18
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17
6
Φ19
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18
18
Φ20
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19
8
Φ21
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20
12
Φ22
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, 21
10
Φ23
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, 21,22
22
Φ24
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, 21,22,23
8
Φ25
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24
20
Φ26
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25
12
Φ27
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26
18
Φ28
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27
12
Φ29
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, 21,
22,23,24,25,26,27,28