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Fully multiplicative with a(A027697(k)) = A027699(k) and a(A027699(k)) = A027697(k) for any k > 0.
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%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