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A222266 Irregular triangle which lists the bi-unitary divisors of n in row n. 15
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: A049077 A180184 A330752 * A077609 A077610 A329534

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 June 12 08:13 EDT 2021. Contains 344943 sequences. (Running on oeis4.)