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%I #11 Apr 20 2017 12:34:06
%S 1,16,2,8,4,12,20,24,6,27,3,32,5,48,7,64,9,18,36,28,40,10,56,14,72,22,
%T 80,11,81,13,96,15,54,21,108,30,88,26,104,34,112,17,128,19,144,23,160,
%U 25,50,75,100,44,52,60,68,76,84,92,116,120,38,136,42,135,33
%N Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^4 for some prime p.
%C This sequence is a permutation of the natural numbers.
%H Rémy Sigrist, <a href="/A285386/b285386.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A285386/a285386.txt">C++ program for A285386</a>
%H Rémy Sigrist, <a href="/A285386/a285386.png">Scatterplot of the first 100000 terms</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^4 divides a(n)*a(n+1), are:
%e n a(n) p
%e -- ---- -
%e 1 1 2
%e 2 16 2
%e 3 2 2
%e 4 8 2
%e 5 4 2
%e 6 12 2
%e 7 20 2
%e 8 24 2
%e 9 6 3
%e 10 27 3
%e 11 3 2
%e 12 32 2
%e 13 5 2
%e 14 48 2
%e 15 7 2
%e 16 64 2
%e 17 9 3
%e 18 18 3
%e 19 36 2
%e 20 28 2
%e ...
%e 165 95 2
%e 166 432 2, 3
%e 167 87 3
%e ...
%Y Cf. A285296.
%K nonn
%O 1,2
%A _Rémy Sigrist_, Apr 18 2017
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