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A206778 Irregular triangle in which n-th row lists squarefree divisors (A005117) of n.

%I A206778 #23 May 02 2025 03:07:53
%S A206778 1,1,2,1,3,1,2,1,5,1,2,3,6,1,7,1,2,1,3,1,2,5,10,1,11,1,2,3,6,1,13,1,2,
%T A206778 7,14,1,3,5,15,1,2,1,17,1,2,3,6,1,19,1,2,5,10,1,3,7,21,1,2,11,22,1,23,
%U A206778 1,2,3,6,1,5,1,2,13,26,1,3,1,2,7,14,1,29
%N A206778 Irregular triangle in which n-th row lists squarefree divisors (A005117) of n.
%H A206778 Reinhard Zumkeller, <a href="/A206778/b206778.txt">Rows n=1..1000 of triangle, flattened</a>
%e A206778 Triangle begins:
%e A206778 .   1: [1]
%e A206778 .   2: [1, 2]
%e A206778 .   3: [1, 3]
%e A206778 .   4: [1, 2]
%e A206778 .   5: [1, 5]
%e A206778 .   6: [1, 2, 3, 6]
%e A206778 .   7: [1, 7]
%e A206778 .   8: [1, 2]
%e A206778 .   9: [1, 3]
%e A206778 .  10: [1, 2, 5, 10]
%e A206778 .  11: [1, 11]
%e A206778 .  12: [1, 2, 3, 6].
%p A206778 A206778 := proc(n)
%p A206778     local sqdvs ,nfac,d;
%p A206778     sqdvs := {} ;
%p A206778     nfac := ifactors(n)[2] ;
%p A206778     for d in numtheory[divisors](n) do
%p A206778         if issqrfree(d) then
%p A206778             sqdvs := sqdvs union {d} ;
%p A206778         end if;
%p A206778     end do:
%p A206778     sort(sqdvs) ;
%p A206778 end proc:
%p A206778 seq(op(A206778(n)),n=1..10) ; # _R. J. Mathar_, Mar 06 2023
%t A206778 Flatten[Table[Select[Divisors[n],SquareFreeQ],{n,30}]] (* _Harvey P. Dale_, Apr 11 2012 *)
%o A206778 (Haskell)
%o A206778 a206778 n k = a206778_row n !! k
%o A206778 a206778_row = filter ((== 1) . a008966) . a027750_row
%o A206778 a206778_tabf = map a206778_row [1..]
%o A206778 -- _Reinhard Zumkeller_, May 03 2013, Feb 12 2012
%o A206778 (PARI) row(n) = select(x -> issquarefree(x), divisors(n)); \\ _Amiram Eldar_, May 02 2025
%Y A206778 Cf. A008966, A034444 (row lengths), A048250 (row sums), A206787; A077610.
%Y A206778 Cf. A027750, A050320, A050326, A050328.
%K A206778 nonn,tabf
%O A206778 1,3
%A A206778 _Reinhard Zumkeller_, Feb 12 2012