

A128487


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


3



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
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OFFSET

2,3


COMMENTS

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


LINKS



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(n1, 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



KEYWORD

nonn,tabf


AUTHOR



EXTENSIONS



STATUS

approved



