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A070920
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a(n) = Card{ (x,y,z,u) | lcm(x,y,z,u)=n }.
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5
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1, 15, 15, 65, 15, 225, 15, 175, 65, 225, 15, 975, 15, 225, 225, 369, 15, 975, 15, 975, 225, 225, 15, 2625, 65, 225, 175, 975, 15, 3375, 15, 671, 225, 225, 225, 4225, 15, 225, 225, 2625, 15, 3375, 15, 975, 975, 225, 15, 5535, 65, 975, 225, 975, 15, 2625, 225
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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)^4/k^s.
Multiplicative with a(p^e) = (e+1)^4 - e^4. - Amiram Eldar, Sep 03 2023
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MATHEMATICA
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Join[{1}, Table[Product[(k + 1)^4 - k^4, {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)^4*moebius(n/d)), ", "))
(PARI) a(n) = vecprod(apply(x->(x+1)^4-x^4, 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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