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A159253
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a(n) is the smallest positive integer not yet in the sequence such that n * a(n) is a cube.
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2
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1, 4, 9, 2, 25, 36, 49, 8, 3, 100, 121, 18, 169, 196, 225, 32, 289, 12, 361, 50, 441, 484, 529, 72, 5, 676, 27, 98, 841, 900, 961, 16, 1089, 1156, 1225, 6, 1369, 1444, 1521, 200, 1681, 1764, 1849, 242, 75, 2116, 2209, 288, 7, 20, 2601, 338, 2809, 108, 3025, 392
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OFFSET
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1,2
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COMMENTS
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This is a self-inverse permutation of the positive integers.
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LINKS
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FORMULA
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Multiplicative with a(p^{3n}) = p^{3n}, a(p^{3n+1}) = p^{3n+2), and a(p^{3n+2)) = p^{3n+1).
Sum_{k=1..n} a(k) ~ c * n^3, where c = (zeta(6)/(3*zeta(3))) * Product_{p prime} (1 - 1/p^2 + 1/p^3) = A347328 * A330596 / 3 = 0.2111705... . - Amiram Eldar, Dec 01 2022
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MATHEMATICA
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f[p_, e_] := If[(r = Mod[e, 3]) == 0, p^e, p^(e - (-1)^r)]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)
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PROG
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(PARI) a(n) = {my(f = factor(n), r); prod(i = 1, #f~, r=f[i, 2]%3; f[i, 1]^if(r == 0, f[i, 2], f[i, 2]-(-1)^r)); } \\ Amiram Eldar, Dec 01 2022
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CROSSREFS
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Cf. A064429 (function on exponents)
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KEYWORD
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mult,nonn
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AUTHOR
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STATUS
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approved
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