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A222266 Irregular triangle which lists the bi-unitary divisors of n in row n. 7
1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 9, 1, 2, 5, 10, 1, 11, 1, 3, 4, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 2, 8, 16, 1, 17, 1, 2, 9, 18, 1, 19, 1, 4, 5, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 4, 6, 8, 12, 24, 1, 25, 1, 2, 13, 26, 1, 3, 9, 27, 1, 4, 7, 28, 1, 29, 1, 2, 3, 5, 6, 10, 15, 30, 1, 31, 1, 2, 4, 8, 16, 32, 1, 3, 11, 33, 1, 2, 17, 34, 1, 5, 7, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The bi-unitary divisors of n are the divisors of n such that the largest common unitary divisor of d and n/d is 1, indicated by A165430.

The first difference from the triangle A077609 is in row n=16.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..13171 (rows 1 <= n <= 2000).

EXAMPLE

The Table starts

1;

1, 2;

1, 3;

1, 4;

1, 5;

1, 2, 3, 6;

1, 7;

1, 2, 4, 8;

1, 9;

1, 2, 5, 10;

1, 11;

1, 3, 4, 12;

1, 13;

1, 2, 7, 14;

1, 3, 5, 15;

1, 2, 8, 16;

1, 17;

MAPLE

# Return set of unitary divisors of n.

A077610_row := proc(n)

    local u, d ;

    u := {} ;

    for d in numtheory[divisors](n) do

        if igcd(n/d, d) = 1 then

            u := u union {d} ;

        end if;

    end do:

    u ;

end proc:

# true if d is a bi-unitary divisor of n.

isbiudiv := proc(n, d)

    if n mod d = 0 then

        A077610_row(d) intersect A077610_row(n/d) ;

        if % = {1} then

            true;

        else

            false;

        end if;

    else

        false;

    end if;

end proc:

# Return set of bi-unitary divisors of n

biudivs := proc(n)

    local u, d ;

    u := {} ;

    for d in numtheory[divisors](n) do

        if isbiudiv(n, d) then

            u := u union {d} ;

        end if;

    end do:

    u ;

end proc:

for n from 1 to 35 do

    print(op(biudivs(n))) ;

end do:

MATHEMATICA

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; Table[Function[d, Union@ Flatten@ Select[Transpose@ {d, n/d}, Last@ Intersection[f@ #1, f@ #2] == 1 & @@ # &]]@ Select[Divisors@ n, # <= Floor@ Sqrt@ n &], {n, 35}] (* Michael De Vlieger, May 07 2017 *)

CROSSREFS

Cf. A188999 (row sums), A286324 (row lengths).

Sequence in context: A085343 A049077 A180184 * A077609 A077610 A317746

Adjacent sequences:  A222263 A222264 A222265 * A222267 A222268 A222269

KEYWORD

nonn,tabf

AUTHOR

R. J. Mathar, May 05 2013

STATUS

approved

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Last modified October 14 15:12 EDT 2019. Contains 328019 sequences. (Running on oeis4.)