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%I #25 May 04 2016 03:29:18
%S 1,2,3,4,5,6,7,12,8,9,10,14,16,11,24,13,36,15,18,17,48,19,60,20,25,28,
%T 30,21,40,32,44,64,22,72,23,81,26,80,27,100,29,120,31,144,33,168,34,
%U 180,35,192,37,240,38,324,41,252,42,49,54,56,84,39,336,43
%N a(1) = 1. a(n) = the smallest integer not yet occurring such that if d(a(n)) = d(a(k)), then d(a(n-1)) doesn't equal d(a(k-1)) for any k where 2<= k <= n-1, where d(m) = the number of divisors of m.
%C This sequence is a permutation of the positive integers.
%C The derived sequence 2^d(a(n))*3^d(a(n+1)), where d(m) = the number of divisors of m, contains only distinct terms. - _Paul Tek_, Mar 05 2014
%H Paul Tek, <a href="/A175500/b175500.txt">Table of n, a(n) for n = 1..2473</a>
%H Paul Tek, <a href="/A175500/a175500.txt">C++ program for this sequence</a>
%o (PARI) ok(j, va, vs, n) = {if (vecsearch(vs, j), return (0)); for (k=1, n-1, if ((numdiv(j) == numdiv(va[k])) && (numdiv(va[k-1]) == numdiv(va[n-1])), return (0));); 1;}
%o findnew(va, vs, n) = {my(j = 1); my(vs = vecsort(va)); until (ok(j, va, vs, n), j++); j;}
%o lista(nn) = {my(va = [1]); for (n=2, nn, vs = vecsort(va); newa = findnew(va, vs, n); va = concat(va, newa);); va;} \\ _Michel Marcus_, May 04 2016
%Y Cf. A175501, A175502
%K nonn,look
%O 1,2
%A _Leroy Quet_, May 31 2010
%E a(26)-a(64) from _Paul Tek_, Mar 05 2014
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