fareylen

fareylen
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fareylen — returns the length of a Farey Sequence.

Description

This opcode can be used in conjunction with GENfarey. It calculates the length of Farey Sequence F_n. Its length is given by: |F_n| = 1 + SUM over n phi(m) where phi(m) is Euler's totient function, which gives the number of integers ≤ m that are coprime to m.

Some values for the length of F_n given n:

n	F_n
1	2
2	3
3	5
4	7
5	11
6	13
7	19
8	23
9	29
10	33
11	43
12	47
13	59
14	65
15	73
16	81
17	97
18	103
19	121
20	129

Syntax

kfl fareylen kfn

Performance

The length of the identified Farey sequence is returned.

kfn -- Integer identifying the sequence.

Credits

Author: Georg Boenn

University of Glamorgan, UK

New in Csound version 5.13

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n	F_n
1	2
2	3
3	5
4	7
5	11
6	13
7	19
8	23
9	29
10	33
11	43
12	47
13	59
14	65
15	73
16	81
17	97
18	103
19	121
20	129

n	F_n
1	2
2	3
3	5
4	7
5	11
6	13
7	19
8	23
9	29
10	33
11	43
12	47
13	59
14	65
15	73
16	81
17	97
18	103
19	121
20	129

n	F_n
1	2
2	3
3	5
4	7
5	11
6	13
7	19
8	23
9	29
10	33
11	43
12	47
13	59
14	65
15	73
16	81
17	97
18	103
19	121
20	129