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%I #11 Apr 24 2017 00:26:03
%S 1,36,2,18,4,9,8,25,12,3,24,6,30,10,20,5,40,15,45,16,27,28,7,56,14,42,
%T 21,48,33,44,11,72,13,52,26,50,22,54,32,49,60,35,63,64,75,39,78,66,84,
%U 51,68,17,100,19,76,38,90,34,98,46,92,23,108,29,116,58
%N Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^2 for at least two distinct primes p.
%C The sequence can always be extended with a multiple of 36; after a multiple of 36, we can extend the sequence with the least unused number; as there are infinitely many multiples of 36, this sequence is a permutation of the natural numbers (with inverse A285576).
%C For any k>=0, let c_k be the lexicographically earliest sequence of distinct terms such that the product of two consecutive terms is divisible by p^2 for at least k distinct primes p; in particular we have:
%C - c_0 = A000027 (the natural numbers),
%C - c_1 = A285296,
%C - c_2 = a (this sequence).
%C For any k>=0, c_k is a permutation of the natural numbers.
%H Rémy Sigrist, <a href="/A285575/b285575.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A285575/a285575.gp.txt">PARI program for A285575</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The first terms, alongside the primes p such that p^2 divides a(n)*a(n+1), are:
%e n a(n) p
%e -- ---- ----
%e 1 1 2, 3
%e 2 36 2, 3
%e 3 2 2, 3
%e 4 18 2, 3
%e 5 4 2, 3
%e 6 9 2, 3
%e 7 8 2, 5
%e 8 25 2, 5
%e 9 12 2, 3
%e 10 3 2, 3
%e 11 24 2, 3
%e 12 6 2, 3
%e 13 30 2, 5
%e 14 10 2, 5
%e 15 20 2, 5
%e 16 5 2, 5
%e 17 40 2, 5
%e 18 15 3, 5
%e 19 45 2, 3
%e 20 16 2, 3
%e ...
%e 115 160 2, 5
%e 116 115 2, 3, 5
%e 117 180 2, 3
%e ...
%Y Cf. A285296, A285576 (inverse).
%K nonn,look
%O 1,2
%A _Rémy Sigrist_, Apr 22 2017
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