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

%I A128487 #20 Sep 20 2024 03:21:00
%S A128487 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 A128487 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 A128487 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 A128487 Irregular array where n-th row is the positive integers < n which are coprime to exactly one distinct prime divisor of n.
%C A128487 Number of terms in n-th row is A126080(n). Row 1 has zero terms, so the first listed row is row 2.
%e A128487 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 A128487 First few rows of the triangle:
%e A128487   1;
%e A128487   1, 2;
%e A128487   1, 3;
%e A128487   1, 2, 3, 4;
%e A128487   2, 3, 4;
%e A128487   1, 2, 3, 4, 5, 6;
%e A128487   1, 3, 5, 7;
%e A128487   1, 2, 4, 5, 7, 8;
%e A128487   2, 4, 5, 6, 8;
%e A128487   1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
%e A128487   2, 3, 4, 8, 9, 10;
%e A128487   1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;
%e A128487   ...
%o A128487 (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 A128487 tabf(nn) = for (n=1, nn, print(row(n))); \\ _Michel Marcus_, Oct 25 2017
%Y A128487 Cf. A126080, A128488.
%K A128487 nonn,tabf
%O A128487 2,3
%A A128487 _Leroy Quet_, Mar 04 2007
%E A128487 More terms from _R. J. Mathar_, Oct 08 2007