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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-François 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 A322313 A322315 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 December 12 23:01 EST 2018. Contains 318081 sequences. (Running on oeis4.)