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 A383279 #10 Apr 22 2025 02:43:27
%S A383279 1,2,3,4,5,7,8,9,11,6,13,16,17,19,10,23,12,25,27,14,29,15,31,32,18,37,
%T A383279 20,41,21,43,22,47,24,49,26,53,28,59,61,64,33,67,34,35,71,36,73,38,39,
%U A383279 79,40,81,83,44,89,45,46,48,97,50,101,51,103,52,107,54,109
%N A383279 The unique solution to x * A034444(x) = A383276(n).
%C A383279 a(n) is the single divisor d of A383276(n) such that d * A034444(d) = A383276(n).
%C A383279 A permutation of the positive integers: the positive integers k sort by the value of k * A034444(k).
%H A383279 Amiram Eldar, <a href="/A383279/b383279.txt">Table of n, a(n) for n = 1..10000</a>
%H A383279 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%F A383279 a(n) * A034444(a(n)) = A383276(n).
%F A383279 Let m = A383276(n). Then, either A007814(m) = A005087(m) and then a(n) = A000265(m), or A007814(m) > A005087(m) + 1 and then a(n) = m / 2^(A005087(m)+1).
%t A383279 s[k_] := Module[{ds = Divisors[k], ans = Nothing}, Do[If[2^PrimeNu[d]*d == k, ans = d; Break[]], {d, ds}]; ans]; Array[s, 300]
%t A383279 (* second program *)
%t A383279 s[k_] := Module[{e = IntegerExponent[k, 2], o, om}, o = k/2^e; om = PrimeNu[o]; If[e == om, o, If[e > om + 1, 2^(e-om-1) * o, Nothing]]]; Array[s, 300]
%o A383279 (PARI) list(lim) = for(k = 1, lim, fordiv(k, d, if((1 << omega(d)) * d == k, print1(d, ", "); break)));
%o A383279 (PARI) list(lim) = {my(e, o, om); for(k = 1, lim, e = valuation(k, 2); o = k >> e; om = omega(o); if(e == om, print1(o, ", "), if(e > om + 1, print1((1 << (e-om-1)) * o, ", "))));}
%Y A383279 Cf. A000265, A005087, A007814, A034444, A383276, A383277, A383278.
%K A383279 nonn,easy
%O A383279 1,2
%A A383279 _Amiram Eldar_, Apr 21 2025