A128487 Irregular array where n-th row is the positive integers < n which are coprime to exactly one distinct prime divisor of n.

1, 1, 2, 1, 3, 1, 2, 3, 4, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 3, 5, 7, 1, 2, 4, 5, 7, 8, 2, 4, 5, 6, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 2, 4, 6, 7, 8, 10, 12, 3, 5, 6, 9, 10, 12, 1, 3, 5, 7, 9, 11, 13, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

Offset: 2

Author

Leroy Quet, Mar 04 2007

Keywords

• nonn
• tabf

Comments

Number of terms in n-th row is A126080(n). Row 1 has zero terms, so the first listed row is row 2.

Examples

			Concerning row 12: 1,5,7,11 don't appear because they are each coprime to 2 AND 3 (the distinct prime divisors of 12). 6 doesn't appear because it is coprime to neither prime dividing 12. The row consists of 2,3,4,8,9,10 because each term is coprime to exactly one prime divisor of 12 (i.e., is coprime to 2 or 3, but not to both).
First few rows of the triangle:
  1;
  1, 2;
  1, 3;
  1, 2, 3, 4;
  2, 3, 4;
  1, 2, 3, 4, 5, 6;
  1, 3, 5, 7;
  1, 2, 4, 5, 7, 8;
  2, 4, 5, 6, 8;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
  2, 3, 4, 8, 9, 10;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;
  ...
		

Crossrefs

Cf. A126080, A128488.

Programs

PARI

row(n) = my(f=factor(n)); Vec(select(x->(x==1), vector(n-1, j, sum(k=1, #f~, gcd(j, f[k,1]) == 1)), 1));
tabf(nn) = for (n=1, nn, print(row(n))); \\ Michel Marcus, Oct 25 2017

Extensions

More terms from R. J. Mathar, Oct 08 2007