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A375615 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, n * a(n) belongs to A055932.

%I A375615 #15 May 07 2025 12:26:20
%S A375615 1,2,4,3,6,5,30,8,10,9,210,12,2310,15,14,16,30030,18,510510,21,20,105,
%T A375615 9699690,24,36,1155,32,45,223092870,7,6469693230,27,70,15015,42,25,
%U A375615 200560490130,255255,770,48,7420738134810,35,304250263527210,315,28,4849845
%N A375615 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, n * a(n) belongs to A055932.
%C A375615 This sequence is a self-inverse permutation of the positive integers.
%C A375615 The n-th term is a multiple of A083720(n).
%H A375615 Rémy Sigrist, <a href="/A375615/a375615.gp.txt">PARI program</a>
%H A375615 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A375615 The first terms, alongside the prime factors of n*a(n), are:
%e A375615   n   a(n)  Prime factors
%e A375615   --  ----  --------------------
%e A375615    1     1  {}
%e A375615    2     2  {2}
%e A375615    3     4  {2, 3}
%e A375615    4     3  {2, 3}
%e A375615    5     6  {2, 3, 5}
%e A375615    6     5  {2, 3, 5}
%e A375615    7    30  {2, 3, 5, 7}
%e A375615    8     8  {2}
%e A375615    9    10  {2, 3, 5}
%e A375615   10     9  {2, 3, 5}
%e A375615   11   210  {2, 3, 5, 7, 11}
%e A375615   12    12  {2, 3}
%e A375615   13  2310  {2, 3, 5, 7, 11, 13}
%e A375615   14    15  {2, 3, 5, 7}
%e A375615   15    14  {2, 3, 5, 7}
%o A375615 (PARI) \\ See Links section.
%Y A375615 Cf. A055932, A083720, A375579.
%K A375615 nonn
%O A375615 1,2
%A A375615 _Rémy Sigrist_, Aug 21 2024