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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Row n is a subset of A038566(n) such that the union of a(n) and A112484(n) = A038566(n). Row lengths are A048864(n) = A000010(n)-(A000720(n)-A001221(n)), i.e., phi(n)-(pi(n)-omega(n)). 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 Michael De Vlieger, Table of n, a(n) for n = 1..11055 (rows 1 <= n <= 240) 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))) for n in range(1, 21): print a(n) # Indranil Ghosh, Apr 26 2017 CROSSREFS Cf. A038566, A048597, A048864, A112484. Sequence in context: A222360 A222371 A222479 * A293434 A091570 A116669 Adjacent sequences: A285785 A285786 A285787 * A285789 A285790 A285791 KEYWORD nonn,easy,tabf AUTHOR Michael De Vlieger, Apr 26 2017 STATUS approved

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Last modified August 13 07:44 EDT 2024. Contains 375113 sequences. (Running on oeis4.)