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A295908 Triangle in which n-th row lists divisors d of n such that n/d is squarefree.

%I A295908 #5 Dec 02 2017 03:09:47
%S A295908 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 A295908 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 A295908 1,23,4,8,12,24,5,25,1,2,13,26,9,27,2,4,14,28
%N A295908 Triangle in which n-th row lists divisors d of n such that n/d is squarefree.
%C A295908 For any n > 0:
%C A295908 - the n-th row has A034444(n) terms,
%C A295908 - the n-th row has sum A001615(n),
%C A295908 - the n-th row has leading term A003557(n).
%F A295908 T(n, k) = n / A206778(n,  A034444(n) - k + 1) for any n > 0 and k such that 1 <= k <= A034444(n).
%e A295908 Triangle begins:
%e A295908   1:  [1]
%e A295908   2:  [1, 2]
%e A295908   3:  [1, 3]
%e A295908   4:  [2, 4]
%e A295908   5:  [1, 5]
%e A295908   6:  [1, 2, 3, 6]
%e A295908   7:  [1, 7]
%e A295908   8:  [4, 8]
%e A295908   9:  [3, 9]
%e A295908   10: [1, 2, 5, 10]
%e A295908   11: [1, 11]
%e A295908   12: [2, 4, 6, 12]
%e A295908   13: [1, 13]
%e A295908   14: [1, 2, 7, 14]
%e A295908   15: [1, 3, 5, 15]
%e A295908   16: [8, 16]
%e A295908   17: [1, 17]
%e A295908   18: [3, 6, 9, 18]
%e A295908   19: [1, 19]
%e A295908   20: [2, 4, 10, 20]
%o A295908 (PARI) for (n=1, 28, fordiv (n, d, if (issquarefree(n/d), print1 (d ", "))))
%Y A295908 Cf. A001615 (row sums), A003557, A005117, A034444 (row lengths), A206778.
%K A295908 nonn,tabf
%O A295908 1,3
%A A295908 _Rémy Sigrist_, Nov 29 2017