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A326776 a(n) is the smallest divisor of the n-th nonprime number (A018252(n)) not already in the sequence.

%I A326776 #11 Jul 29 2019 17:01:18
%S A326776 1,2,3,4,9,5,6,7,15,8,18,10,21,11,12,25,13,27,14,30,16,33,17,35,36,19,
%T A326776 39,20,42,22,45,23,24,49,50,51,26,54,55,28,57,29,60,31,63,32,65,66,34,
%U A326776 69,70,72,37,75,38,77,78,40,81,41,84,85,43,87,44,90,91
%N A326776 a(n) is the smallest divisor of the n-th nonprime number (A018252(n)) not already in the sequence.
%C A326776 This sequence is a permutation of the natural numbers.
%C A326776 Empirically:
%C A326776 - the subsequence with the terms satisfying a(n) <= n correspond to A093641,
%C A326776 - if a(n) > n, then a(n) = A018252(n),
%C A326776 - these two situations appear as two lines in the scatterplot of the sequence.
%H A326776 Rémy Sigrist, <a href="/A326776/b326776.txt">Table of n, a(n) for n = 1..10000</a>
%H A326776 Rémy Sigrist, <a href="/A326776/a326776.gp.txt">PARI program for A326776</a>
%H A326776 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A326776 The first terms, alongside the divisors of A018252(n), are:
%e A326776   n   a(n)  div(A018252(n))
%e A326776   --  ----  ---------------
%e A326776    1     1  (1)
%e A326776    2     2  (1, 2, 4)
%e A326776    3     3  (1, 2, 3, 6)
%e A326776    4     4  (1, 2, 4, 8)
%e A326776    5     9  (1, 3, 9)
%e A326776    6     5  (1, 2, 5, 10)
%e A326776    7     6  (1, 2, 3, 4, 6, 12)
%e A326776    8     7  (1, 2, 7, 14)
%e A326776    9    15  (1, 3, 5, 15)
%e A326776   10     8  (1, 2, 4, 8, 16)
%o A326776 (PARI) See Links section.
%Y A326776 Cf. A018252, A093641, A111273.
%K A326776 nonn
%O A326776 1,2
%A A326776 _Rémy Sigrist_, Jul 28 2019