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A382377 Lexicographically earliest sequence of distinct positive integers such that the number of distinct prime factors of n and a(n) differ exactly by one.

%I A382377 #12 Mar 26 2025 17:49:09
%S A382377 2,1,6,10,12,3,14,15,18,4,20,5,21,7,8,22,24,9,26,11,13,16,28,17,33,19,
%T A382377 34,23,35,36,38,39,25,27,29,30,40,31,32,37,44,45,46,41,42,43,48,47,50,
%U A382377 49,53,59,51,60,61,64,66,67,52,54,55,70,71,56,73,57,58
%N A382377 Lexicographically earliest sequence of distinct positive integers such that the number of distinct prime factors of n and a(n) differ exactly by one.
%C A382377 A self-inverse permutation of the positive integers.
%H A382377 Rémy Sigrist, <a href="/A382377/b382377.txt">Table of n, a(n) for n = 1..10000</a>
%H A382377 Rémy Sigrist, <a href="/A382377/a382377.gp.txt">PARI program</a>
%H A382377 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A382377 The initial terms are:
%e A382377   n   a(n)  A001221(n)  A001221(a(n))
%e A382377   --  ----  ----------  -------------
%e A382377    1     2           0              1
%e A382377    2     1           1              0
%e A382377    3     6           1              2
%e A382377    4    10           1              2
%e A382377    5    12           1              2
%e A382377    6     3           2              1
%e A382377    7    14           1              2
%e A382377    8    15           1              2
%e A382377    9    18           1              2
%e A382377   10     4           2              1
%e A382377   11    20           1              2
%e A382377   12     5           2              1
%e A382377   13    21           1              2
%e A382377   14     7           2              1
%e A382377   15     8           2              1
%o A382377 (PARI) \\ See Links section.
%Y A382377 Cf. A001221, A382375, A382376.
%K A382377 nonn
%O A382377 1,1
%A A382377 _Rémy Sigrist_, Mar 23 2025