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A338441 Lexicographically earliest sequence of distinct squarefree numbers such that for any prime p, any run of consecutive multiples of p has length exactly 3.

%I A338441 #14 Aug 23 2024 16:04:00
%S A338441 1,2,6,30,15,5,3,21,42,14,10,35,70,154,22,11,7,77,231,33,39,13,26,34,
%T A338441 102,51,57,19,38,46,138,69,66,110,330,105,273,91,65,55,165,429,78,130,
%U A338441 170,85,17,23,115,230,190,114,285,195,455,182,210,390,1365,1001
%N A338441 Lexicographically earliest sequence of distinct squarefree numbers such that for any prime p, any run of consecutive multiples of p has length exactly 3.
%C A338441 This sequence is a squarefree variant of A338338.
%C A338441 Conjecture: this is a permutation of the squarefree numbers (A005117).
%H A338441 Rémy Sigrist, <a href="/A338441/b338441.txt">Table of n, a(n) for n = 1..10000</a>
%H A338441 Rémy Sigrist, <a href="/A338441/a338441.txt">C program for A338441</a>
%e A338441 The first terms, alongside their prime factors, are:
%e A338441   n   a(n)  Prime factors
%e A338441   --  ----  -------------
%e A338441    1     1
%e A338441    2     2  2
%e A338441    3     6  2 3
%e A338441    4    30  2 3 5
%e A338441    5    15    3 5
%e A338441    6     5      5
%e A338441    7     3    3
%e A338441    8    21    3   7
%e A338441    9    42  2 3   7
%e A338441   10    14  2     7
%e A338441   11    10  2   5
%e A338441   12    35      5 7
%e A338441   13    70  2   5 7
%e A338441   14   154  2     7 11
%e A338441   15    22  2       11
%e A338441   16    11          11
%o A338441 (C) // See Links section.
%Y A338441 Cf. A005117, A338338, A338444.
%K A338441 nonn
%O A338441 1,2
%A A338441 _Rémy Sigrist_, Oct 28 2020