Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Feb 16 2023 05:06:31
%S 1,3,2,9,7,6,5,27,4,21,17,18,23,15,14,81,11,12,29,63,10,51,13,54,49,
%T 69,8,45,19,42,43,243,34,33,35,36,53,87,46,189,71,30,31,153,28,39,83,
%U 162,25,147,22,207,37,24,119,135,58,57,89,126,101,129,20,729
%N Fully multiplicative with a(A027697(k)) = A027699(k) and a(A027699(k)) = A027697(k) for any k > 0.
%C In other words, we replace odious prime numbers with evil prime numbers and vice versa.
%C This sequence is a self-inverse permutation of the positive integers.
%H Rémy Sigrist, <a href="/A360648/a360648.png">Scatterplot of (n, a(n)) such that n, a(n) <= 100000</a>
%H Rémy Sigrist, <a href="/A360648/a360648.gp.txt">PARI program</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e For n = 84:
%e - 82 = 2^2 * 3 * 7,
%e - a(2) = a(A027697(1)) = A027699(1) = 3,
%e - a(3) = a(A027699(1)) = A027697(1) = 2,
%e - a(7) = a(A027697(2)) = A027699(2) = 5,
%e - so a(84) = 3^2 * 2 * 5 = 90.
%o (PARI) See Links section.
%Y Cf. A061898, A027697, A027699, A341090.
%K nonn,base,mult
%O 1,2
%A _Rémy Sigrist_, Feb 15 2023