This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A159253 #14 Feb 04 2025 05:42:22
%S A159253 1,4,9,2,25,36,49,8,3,100,121,18,169,196,225,32,289,12,361,50,441,484,
%T A159253 529,72,5,676,27,98,841,900,961,16,1089,1156,1225,6,1369,1444,1521,
%U A159253 200,1681,1764,1849,242,75,2116,2209,288,7,20,2601,338,2809,108,3025,392
%N A159253 a(n) is the smallest positive integer not yet in the sequence such that n * a(n) is a cube.
%C A159253 This is a self-inverse permutation of the positive integers.
%H A159253 Amiram Eldar, <a href="/A159253/b159253.txt">Table of n, a(n) for n = 1..10000</a>
%F A159253 Multiplicative with a(p^(3*n)) = p^(3*n), a(p^(3*n+1)) = p^(3*n+2), and a(p^(3*n+2)) = p^(3*n+1).
%F A159253 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
%t A159253 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 *)
%o A159253 (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
%Y A159253 Cf. A064429 (function on exponents)
%Y A159253 Cf. A330596, A347328.
%K A159253 mult,nonn,easy
%O A159253 1,2
%A A159253 _Franklin T. Adams-Watters_, Apr 07 2009