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A382375 Lexicographically earliest sequence of distinct positive integers such that the number of prime factors counted with multiplicity of n and a(n) differ exactly by one.

%I A382375 #11 Mar 26 2025 20:56:04
%S A382375 2,1,4,3,6,5,9,10,7,8,14,15,21,11,12,18,22,16,25,24,13,17,26,20,19,23,
%T A382375 33,34,35,36,38,40,27,28,29,30,39,31,37,32,46,49,51,54,55,41,57,56,42,
%U A382375 58,43,60,62,44,45,48,47,50,65,52,69,53,74,72,59,77,82
%N A382375 Lexicographically earliest sequence of distinct positive integers such that the number of prime factors counted with multiplicity of n and a(n) differ exactly by one.
%C A382375 A self-inverse permutation of the positive integers.
%H A382375 Rémy Sigrist, <a href="/A382375/b382375.txt">Table of n, a(n) for n = 1..10000</a>
%H A382375 Rémy Sigrist, <a href="/A382375/a382375.gp.txt">PARI program</a>
%H A382375 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A382375 The initial terms are:
%e A382375   n   a(n)  A001222(n)  A001222(a(n))
%e A382375   --  ----  ----------  -------------
%e A382375    1     2           0              1
%e A382375    2     1           1              0
%e A382375    3     4           1              2
%e A382375    4     3           2              1
%e A382375    5     6           1              2
%e A382375    6     5           2              1
%e A382375    7     9           1              2
%e A382375    8    10           3              2
%e A382375    9     7           2              1
%e A382375   10     8           2              3
%e A382375   11    14           1              2
%e A382375   12    15           3              2
%e A382375   13    21           1              2
%e A382375   14    11           2              1
%e A382375   15    12           2              3
%o A382375 (PARI) \\ See Links section.
%Y A382375 Cf. A001222, A382374, A382377.
%K A382375 nonn
%O A382375 1,1
%A A382375 _Rémy Sigrist_, Mar 23 2025