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A086165
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a(n) = Card{ (x,y,z) | x < y < z and lcm(x,y,z) = n}.
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3
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0, 0, 0, 1, 0, 4, 0, 3, 1, 4, 0, 15, 0, 4, 4, 6, 0, 15, 0, 15, 4, 4, 0, 33, 1, 4, 3, 15, 0, 44, 0, 10, 4, 4, 4, 48, 0, 4, 4, 33, 0, 44, 0, 15, 15, 4, 0, 58, 1, 15, 4, 15, 0, 33, 4, 33, 4, 4, 0, 133, 0, 4, 15, 15, 4, 44, 0, 15, 4, 44, 0, 100, 0, 4, 15, 15, 4, 44, 0, 58, 6, 4, 0, 133, 4, 4, 4, 33, 0
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OFFSET
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1,6
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LINKS
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FORMULA
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MAPLE
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for n from 1 to 100 do a[n] := 0:for x from 1 to n do for y from x+1 to n do for z from y+1 to n do if(lcm(x, y, z)=n) then a[n] := a[n]+1:fi:od:od:od:od:seq(a[j], j=1..200); # Sascha Kurz, Sep 22 2003
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MATHEMATICA
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f1[p_, e_] := (e+1)^3 - e^3; f2[p_, e_] := 2*e + 1; a[1] = 0; a[n_] := (Times @@ f1 @@@ (f = FactorInteger[n]) - 3 * Times @@ f2 @@@f + 2) / 6; Array[a, 100] (* Amiram Eldar, Sep 03 2023 *)
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PROG
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(PARI)
A070919(n) = sumdiv(n, d, (numdiv(d)^3)*moebius(n/d));
(PARI) a(n) = {my(e = factor(n)[, 2]); (vecprod(apply(x->(x+1)^3-x^3, e)) - 3*vecprod(apply(x->2*x+1, e)) + 2) / 6; } \\ Amiram Eldar, Sep 03 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 13 2003
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EXTENSIONS
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STATUS
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approved
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