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A338444 Lexicographically earliest sequence of distinct squarefree numbers such that for any prime p, any run of consecutive multiples of p has length exactly 2.

%I A338444 #13 Aug 23 2024 15:55:33
%S A338444 1,2,6,3,5,10,14,7,11,22,26,13,15,30,34,17,19,38,42,21,23,46,58,29,31,
%T A338444 62,66,33,35,70,74,37,39,78,82,41,43,86,94,47,51,102,106,53,55,110,
%U A338444 114,57,59,118,122,61,65,130,134,67,69,138,142,71,73,146,154,77
%N A338444 Lexicographically earliest sequence of distinct squarefree numbers such that for any prime p, any run of consecutive multiples of p has length exactly 2.
%C A338444 This sequence is a squarefree variant of A280864.
%C A338444 Conjecture: this sequence is a permutation of the squarefree numbers (A005117).
%H A338444 Rémy Sigrist, <a href="/A338444/b338444.txt">Table of n, a(n) for n = 1..10000</a>
%H A338444 Rémy Sigrist, <a href="/A338444/a338444.txt">C program for A338444</a>
%e A338444 The first terms, alongside their prime factors, are:
%e A338444   n   a(n)  Prime factors
%e A338444   --  ----  -------------
%e A338444    1     1
%e A338444    2     2  2
%e A338444    3     6  2 3
%e A338444    4     3    3
%e A338444    5     5      5
%e A338444    6    10  2   5
%e A338444    7    14  2     7
%e A338444    8     7        7
%e A338444    9    11          11
%e A338444   10    22  2       11
%e A338444   11    26  2         13
%e A338444   12    13            13
%e A338444   13    15    3 5
%e A338444   14    30  2 3 5
%e A338444   15    34  2           17
%e A338444   16    17              17
%o A338444 (C) // See Links section.
%Y A338444 Cf. A005117, A280864, A338441.
%K A338444 nonn
%O A338444 1,2
%A A338444 _Rémy Sigrist_, Oct 28 2020