login
Triangle in which n-th row lists divisors d of n such that n/d is squarefree.
0

%I #5 Dec 02 2017 03:09:47

%S 1,1,2,1,3,2,4,1,5,1,2,3,6,1,7,4,8,3,9,1,2,5,10,1,11,2,4,6,12,1,13,1,

%T 2,7,14,1,3,5,15,8,16,1,17,3,6,9,18,1,19,2,4,10,20,1,3,7,21,1,2,11,22,

%U 1,23,4,8,12,24,5,25,1,2,13,26,9,27,2,4,14,28

%N Triangle in which n-th row lists divisors d of n such that n/d is squarefree.

%C For any n > 0:

%C - the n-th row has A034444(n) terms,

%C - the n-th row has sum A001615(n),

%C - the n-th row has leading term A003557(n).

%F T(n, k) = n / A206778(n, A034444(n) - k + 1) for any n > 0 and k such that 1 <= k <= A034444(n).

%e Triangle begins:

%e 1: [1]

%e 2: [1, 2]

%e 3: [1, 3]

%e 4: [2, 4]

%e 5: [1, 5]

%e 6: [1, 2, 3, 6]

%e 7: [1, 7]

%e 8: [4, 8]

%e 9: [3, 9]

%e 10: [1, 2, 5, 10]

%e 11: [1, 11]

%e 12: [2, 4, 6, 12]

%e 13: [1, 13]

%e 14: [1, 2, 7, 14]

%e 15: [1, 3, 5, 15]

%e 16: [8, 16]

%e 17: [1, 17]

%e 18: [3, 6, 9, 18]

%e 19: [1, 19]

%e 20: [2, 4, 10, 20]

%o (PARI) for (n=1, 28, fordiv (n, d, if (issquarefree(n/d), print1 (d ", "))))

%Y Cf. A001615 (row sums), A003557, A005117, A034444 (row lengths), A206778.

%K nonn,tabf

%O 1,3

%A _Rémy Sigrist_, Nov 29 2017