

A285788


Irregular triangle T(n,m): nonprime 1 <= k <= n such that n and k are coprime.


1



1, 1, 1, 1, 1, 4, 1, 1, 4, 6, 1, 1, 4, 8, 1, 9, 1, 4, 6, 8, 9, 10, 1, 1, 4, 6, 8, 9, 10, 12, 1, 9, 1, 4, 8, 14, 1, 9, 15, 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 1, 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 1, 9, 1, 4, 8, 10, 16, 20, 1, 9, 15, 21, 1, 4, 6, 8, 9, 10
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OFFSET

1,6


COMMENTS

1 appears in every row since 1 is not prime and coprime to all n.
4 is the smallest composite and appears first in row 5 since 4 divides 4.
Rows that contain the single term 1 are in A048597; the largest n = 30 such that the only term is 1.
For prime p, row p contains 1 and all composites k < p, since 1 < m < p are coprime to p.


LINKS



EXAMPLE

Triangle begins:
n\m 1 2 3 4 5 6 7
1: 1
2: 1
3: 1
4: 1
5: 1 4
6: 1
7: 1 4 6
8: 1
9: 1 4 8
10: 1 9
11: 1 4 6 8 9 10
12: 1
13: 1 4 6 8 9 10 12
14: 1 9
15: 1 4 8 14
16: 1 9 15
...


MATHEMATICA

Table[Select[Range@ n, And[! PrimeQ@ #, CoprimeQ[#, n]] &], {n, 23}] // Flatten


PROG

(Python)
from sympy import gcd, isprime
def a(n): return list(filter(lambda k: isprime(k)==0 and gcd(k, n)==1, range(1, n + 1)))


CROSSREFS



KEYWORD

nonn,easy,tabf


AUTHOR



STATUS

approved



