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

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, 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, 1, 2, 3, 6, 1, 5, 1, 2, 13, 26, 1, 3, 1, 2, 7, 14, 1, 29

Offset: 1

Author

Reinhard Zumkeller, Feb 12 2012

Keywords

• nonn
• tabf

Examples

			Triangle begins:
.   1: [1]
.   2: [1, 2]
.   3: [1, 3]
.   4: [1, 2]
.   5: [1, 5]
.   6: [1, 2, 3, 6]
.   7: [1, 7]
.   8: [1, 2]
.   9: [1, 3]
.  10: [1, 2, 5, 10]
.  11: [1, 11]
.  12: [1, 2, 3, 6].
		

Links

• Reinhard Zumkeller, Rows n=1..1000 of triangle, flattened

Crossrefs

Cf. A008966, A034444 (row lengths), A048250 (row sums), A206787; A077610.

Cf. A027750, A050320, A050326, A050328.

Programs

Haskell

a206778 n k = a206778_row n !! k
a206778_row = filter ((== 1) . a008966) . a027750_row
a206778_tabf = map a206778_row [1..]
-- Reinhard Zumkeller, May 03 2013, Feb 12 2012

Maple

A206778 := proc(n)
    local sqdvs ,nfac,d;
    sqdvs := {} ;
    nfac := ifactors(n)[2] ;
    for d in numtheory[divisors](n) do
        if issqrfree(d) then
            sqdvs := sqdvs union {d} ;
        end if;
    end do:
    sort(sqdvs) ;
end proc:
seq(op(A206778(n)),n=1..10) ; # R. J. Mathar, Mar 06 2023

Mathematica

Flatten[Table[Select[Divisors[n],SquareFreeQ],{n,30}]] (* Harvey P. Dale, Apr 11 2012 *)

PARI

row(n) = select(x -> issquarefree(x), divisors(n)); \\ Amiram Eldar, May 02 2025