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 A071694 Number of ways to write n as n = x*y*z/(x+y+z) 1 <= x <= y <= z <= n. 1
 0, 0, 1, 0, 1, 0, 1, 2, 2, 1, 2, 3, 1, 3, 5, 3, 2, 3, 2, 7, 5, 1, 3, 8, 2, 4, 8, 4, 3, 5, 2, 9, 5, 2, 14, 12, 1, 4, 10, 10, 3, 5, 2, 11, 11, 2, 4, 13, 5, 10, 8, 6, 3, 14, 12, 22, 5, 1, 5, 14, 1, 5, 22, 11, 13, 11, 2, 11, 9, 6, 5, 19, 1, 5, 19, 10, 13, 6, 4, 33, 14, 1, 5, 24, 6, 6, 11, 10, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS If n is a prime other than 3, then a(n) = A000005(n+1)/2 - 1. - Robert Israel, Oct 29 2018 LINKS Robert Israel, Table of n, a(n) for n = 1..1000 MAPLE f:= proc(n) local x, y, z, t; t:= 0; for x from 1 to n do for y from max(x, ceil(n/x)) to n do if x*y = n then next fi; z:= n*(x+y)/(x*y-n); if z::integer and z>=y and z<=n then t:= t+1 fi od od: t end proc: map(f, [\$1..100]); # Robert Israel, Oct 29 2018 MATHEMATICA a[n_] := Sum[Boole[x y z/(x + y + z) == n], {x, n}, {y, x}, {z, y}]; Array[a, 100] (* Jean-François Alcover, Aug 24 2020 *) PROG (PARI) for(n=1, 90, print1(sum(a=1, n, sum(b=1, a, sum(c=1, b, if(a*b*c/(a+b+c)-n, 0, 1)))), ", ")) CROSSREFS Cf. A000005, A063520. Sequence in context: A002345 A321325 A233918 * A365393 A366286 A072781 Adjacent sequences: A071691 A071692 A071693 * A071695 A071696 A071697 KEYWORD nonn AUTHOR Benoit Cloitre, Jun 23 2002 STATUS approved

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Last modified March 1 22:23 EST 2024. Contains 370443 sequences. (Running on oeis4.)