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A222266 Irregular triangle which lists the bi-unitary divisors of n in row n. 15

%I

%S 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,

%T 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,

%U 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

%N Irregular triangle which lists the bi-unitary divisors of n in row n.

%C 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.

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

%H Michael De Vlieger, <a href="/A222266/b222266.txt">Table of n, a(n) for n = 1..13171</a> (rows 1 <= n <= 2000).

%e The Table starts

%e 1;

%e 1, 2;

%e 1, 3;

%e 1, 4;

%e 1, 5;

%e 1, 2, 3, 6;

%e 1, 7;

%e 1, 2, 4, 8;

%e 1, 9;

%e 1, 2, 5, 10;

%e 1, 11;

%e 1, 3, 4, 12;

%e 1, 13;

%e 1, 2, 7, 14;

%e 1, 3, 5, 15;

%e 1, 2, 8, 16;

%e 1, 17;

%p # Return set of unitary divisors of n.

%p A077610_row := proc(n)

%p local u,d ;

%p u := {} ;

%p for d in numtheory[divisors](n) do

%p if igcd(n/d,d) = 1 then

%p u := u union {d} ;

%p end if;

%p end do:

%p u ;

%p end proc:

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

%p isbiudiv := proc(n,d)

%p if n mod d = 0 then

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

%p if % = {1} then

%p true;

%p else

%p false;

%p end if;

%p else

%p false;

%p end if;

%p end proc:

%p # Return set of bi-unitary divisors of n

%p biudivs := proc(n)

%p local u,d ;

%p u := {} ;

%p for d in numtheory[divisors](n) do

%p if isbiudiv(n,d) then

%p u := u union {d} ;

%p end if;

%p end do:

%p u ;

%p end proc:

%p for n from 1 to 35 do

%p print(op(biudivs(n))) ;

%p end do:

%t 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 *)

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

%K nonn,tabf

%O 1,3

%A _R. J. Mathar_, May 05 2013

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Last modified July 27 20:33 EDT 2021. Contains 346308 sequences. (Running on oeis4.)