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

2,3

Comments

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

Links

Table of n, a(n) for n=2..97.

Example

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;
  ...

Prog

(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

Crossrefs

Cf. A126080, A128488.

Sequence in context: A293248 A096107 A329585 * A056609 A014673 A346704

Adjacent sequences: A128484 A128485 A128486 * A128488 A128489 A128490

Keyword

nonn,tabf

Author

Leroy Quet, Mar 04 2007

Extensions

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

Status

approved