A128487 - OEIS

%I #20 Sep 20 2024 03:21:00

%S 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,

%T 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,

%U 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

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

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

%e 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).

%e First few rows of the triangle:

%e   1;

%e   1, 2;

%e   1, 3;

%e   1, 2, 3, 4;

%e   2, 3, 4;

%e   1, 2, 3, 4, 5, 6;

%e   1, 3, 5, 7;

%e   1, 2, 4, 5, 7, 8;

%e   2, 4, 5, 6, 8;

%e   1, 2, 3, 4, 5, 6, 7, 8, 9, 10;

%e   2, 3, 4, 8, 9, 10;

%e   1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;

%e   ...

%o (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));

%o tabf(nn) = for (n=1, nn, print(row(n))); \\ _Michel Marcus_, Oct 25 2017

%Y Cf. A126080, A128488.

%K nonn,tabf,changed

%O 2,3

%A _Leroy Quet_, Mar 04 2007

%E More terms from _R. J. Mathar_, Oct 08 2007