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A077610 Triangle in which n-th row lists unitary divisors of n. 34
1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 8, 1, 9, 1, 2, 5, 10, 1, 11, 1, 3, 4, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 16, 1, 17, 1, 2, 9, 18, 1, 19, 1, 4, 5, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 3, 8, 24, 1, 25, 1, 2, 13, 26, 1, 27, 1, 4, 7, 28, 1, 29, 1, 2, 3, 5, 6, 10, 15, 30 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

n-th row = n-th row of A165430 without repetitions. - Reinhard Zumkeller, Mar 04 2013

Denominators of sequence of all positive rational numbers ordered as follows:  let m = p(i(1))^e(i(1))*...*p(i(k))^e(i(k)) be the prime factorization of m.  Let S(m) be the vector of rationals p(i(k+1-j))^e(i(k+1-j))/p(i(j))^e(i(j)) for j = 1..k.  The sequence (a(n)) is the concatenation of vectors S(m) for m = 1, 2, ...; for numerators see A229994. - Clark Kimberling, Oct 31 2013

LINKS

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

Eric Weisstein's World of Mathematics, Unitary Divisor

EXAMPLE

1;

1, 2;

1, 3;

1, 4;

1, 5;

1, 2, 3, 6;

1, 7;

1, 8;

1, 9;

1, 2, 5, 10;

1, 11;

MAPLE

with(numtheory);

# returns the number of unitary divisors of n and a list of them, from N. J. A. Sloane, May 01 2013

f:=proc(n)

local ct, i, t1, ans;

ct:=0; ans:=[];

t1:=divisors(n);

for i from 1 to nops(t1) do

d:=t1[i];

if igcd(d, n/d)=1 then ct:=ct+1; ans:=[op(ans), d]; fi;

od:

RETURN([ct, ans]);

end;

MATHEMATICA

row[n_] := Select[ Divisors[n], GCD[#, n/#] == 1 &]; Table[row[n], {n, 1, 30}] // Flatten (* Jean-Fran├žois Alcover, Oct 22 2012 *)

PROG

(Haskell)

a077610 n k = a077610_row n !! k

a077610_row n = [d | d <- [1..n], let (n', m) = divMod n d,

                     m == 0, gcd d n' == 1]

a077610_tabf = map a077610_row [1..]

-- Reinhard Zumkeller, Feb 12 02

(PARI) row(n)=my(f=factor(n), k=#f~); Set(vector(2^k, i, prod(j=1, k, if(bittest(i, j-1), 1, f[j, 1]^f[j, 2]))))

v=[]; for(n=1, 20, v=concat(v, row(n))); v \\ Charles R Greathouse IV, Sep 02 2015

(PARI) row(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); } \\ Michel Marcus, Oct 11 2015

CROSSREFS

Cf. A037445, A027750, A034444 (row lengths), A034448 (row sums); A206778.

Sequence in context: A180184 A222266 A077609 * A228179 A319338 A177815

Adjacent sequences:  A077607 A077608 A077609 * A077611 A077612 A077613

KEYWORD

nonn,tabf

AUTHOR

Eric W. Weisstein, Nov 11 2002

STATUS

approved

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Last modified November 16 07:06 EST 2018. Contains 317258 sequences. (Running on oeis4.)