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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.)