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A070921
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a(n) = Card{ (x,y,z,u,v) | lcm(x,y,z,u,v)=n }.
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5
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1, 31, 31, 211, 31, 961, 31, 781, 211, 961, 31, 6541, 31, 961, 961, 2101, 31, 6541, 31, 6541, 961, 961, 31, 24211, 211, 961, 781, 6541, 31, 29791, 31, 4651, 961, 961, 961, 44521, 31, 961, 961, 24211, 31, 29791, 31, 6541, 6541, 961, 31, 65131, 211, 6541
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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)^5/k^s.
Multiplicative with a(p^e) = (e+1)^5 - e^5. - Amiram Eldar, Sep 03 2023
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MATHEMATICA
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Join[{1}, Table[Product[(k + 1)^5 - k^5, {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)^5*moebius(n/d)), ", "))
(PARI) a(n) = vecprod(apply(x->(x+1)^5-x^5, 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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