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 A336322 #17 Feb 24 2022 11:32:53
%S A336322 1,2,3,4,6,8,5,16,9,12,10,32,15,24,18,256,30,64,7,48,27,20,14,512,36,
%T A336322 40,81,96,21,128,42,65536,54,60,72,1024,35,120,45,768,70,192,105,80,
%U A336322 162,28,210,131072,25,144,90,160,11,4096,108,1536,135,56,22,2048,33,84,243,4294967296,216,384,66,240,270,288,55,262144,110,168,324,480,50
%N A336322 a(n) = A225546(A122111(n)).
%C A336322 A225546 and A122111 are both self-inverse permutations of the positive integers based on prime factorizations, and they share further common properties. For instance, they map the prime numbers to powers of 2: A225546 maps the k-th prime to 2^2^(k-1), whereas A122111 maps it to 2^k.
%C A336322 In composing these permutations, this sequence maps the list of prime numbers to the squarefree numbers, as listed in A019565; and the "normal" numbers (A055932), as listed in A057335, to ascending powers of 2.
%H A336322 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A336322 a(A033844(m)) = A000040(m+1). [Offset corrected _Peter Munn_, Feb 14 2022]
%F A336322 a(A000040(m)) = A019565(m).
%F A336322 a(A057335(m)) = 2^m.
%F A336322 For m >= 1, a(2^m) = A001146(m-1).
%F A336322 a(A253563(m)) = A334866(m).
%F A336322 From _Peter Munn_, Feb 14 2022: (Start)
%F A336322 a(A253560(n)) = a(n)^2.
%F A336322 For n >= 2, a(A003961(n)) = A331590(a(n), 2^2^(A001222(n)-1)).
%F A336322 a(A350066(n, k)) = A331590(a(n), a(k)).
%F A336322 (End)
%Y A336322 A225546 composed with A122111.
%Y A336322 Sorted even bisection: A335738.
%Y A336322 Sorted odd bisection (excluding 1): A335740.
%Y A336322 Sequences used to express relationship between terms of this sequence: A001222, A003961, A253560, A331590, A350066.
%Y A336322 Sequences of sequences (S_1, S_2, ... S_j) with the property a(S_i) = S_{i+1}, or essentially so: (A033844, A000040, A019565), (A057335, A000079, A001146), (A000244, A011764), (A001248, A334110), (A253563, A334866).
%Y A336322 The inverse permutation, A336321, lists sequences where the property is weaker (between the sets of terms).
%K A336322 nonn
%O A336322 1,2
%A A336322 _Antti Karttunen_ and _Peter Munn_, Jul 17 2020