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A053149
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Smallest cube divisible by n.
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13
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1, 8, 27, 8, 125, 216, 343, 8, 27, 1000, 1331, 216, 2197, 2744, 3375, 64, 4913, 216, 6859, 1000, 9261, 10648, 12167, 216, 125, 17576, 27, 2744, 24389, 27000, 29791, 64, 35937, 39304, 42875, 216, 50653, 54872, 59319, 1000, 68921, 74088, 79507, 10648
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OFFSET
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1,2
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LINKS
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FORMULA
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Multiplicative with a(p^e) = p^(e + ((3-e) mod 3)).
Sum_{n>=1} 1/a(n) = Product_{p prime} ((p^3+2)/(p^3-1)) = 1.655234386560802506... . (End)
Sum_{k=1..n} a(k) ~ c * n^4, where c = (zeta(9)/(4*zeta(3))) * Product_{p prime} (1 - 1/p^2 + 1/p^3) = A013667*A330596/(4*A002117) = 0.1559906... . - Amiram Eldar, Oct 27 2022
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MATHEMATICA
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a[n_] := For[k = 1, True, k++, If[ Divisible[c = k^3, n], Return[c]]]; Table[a[n], {n, 1, 44}] (* Jean-François Alcover, Sep 03 2012 *)
f[p_, e_] := p^(e + Mod[3 - e, 3]); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)
scdn[n_]:=Module[{c=Ceiling[Surd[n, 3]]}, While[!Divisible[c^3, n], c++]; c^3]; Array[scdn, 50] (* Harvey P. Dale, Jun 13 2020 *)
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PROG
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(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^(f[i, 2] + (3-f[i, 2])%3)); } \\ Amiram Eldar, Oct 27 2022
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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