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A070919
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a(n) = Card{ (x,y,z) | lcm(x,y,z)=n }.
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8
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1, 7, 7, 19, 7, 49, 7, 37, 19, 49, 7, 133, 7, 49, 49, 61, 7, 133, 7, 133, 49, 49, 7, 259, 19, 49, 37, 133, 7, 343, 7, 91, 49, 49, 49, 361, 7, 49, 49, 259, 7, 343, 7, 133, 133, 49, 7, 427, 19, 133, 49, 133, 7, 259, 49, 259, 49, 49, 7, 931, 7, 49, 133, 127, 49, 343, 7, 133
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OFFSET
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1,2
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COMMENTS
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A048691(n) gives Card{ (x,y) | lcm(x,y)=n }.
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LINKS
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FORMULA
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Sum_{k>0} a(k)/k^s = (1/zeta(s))*Sum_{k>0} tau(k)^3/k^s.
Multiplicative with a(p^e) = 1+3*e+3*e^2 for prime p and e >= 0. - Werner Schulte, Nov 30 2018
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MATHEMATICA
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Join[{1}, Table[Product[(k + 1)^3 - k^3, {k, FactorInteger[n][[All, 2]]}], {n, 2, 68}]] (* Geoffrey Critzer, Jan 10 2015 *)
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PROG
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(PARI) for(n=1, 100, print1(sumdiv(n, d, numdiv(d)^3*moebius(n/d)), ", "))
(PARI) a(n) = vecprod(apply(x->(x+1)^3-x^3, factor(n)[, 2])); \\ Amiram Eldar, Sep 03 2023
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CROSSREFS
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KEYWORD
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mult,easy,nonn
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AUTHOR
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STATUS
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approved
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