%I #19 Jan 04 2019 19:00:10
%S 174,422,474,602,831,843,930,1074,1182,1322,1374,1443,1518,1623,1803,
%T 1974,2006,2022,2222,2274,2298,2522,2526,2595,2694,2870,2874,3122,
%U 3210,3282,3423,3478,3574,3702,3770,3774,4022,4074,4202,4323,4359,4458,4474
%N Lesser of two successive squarefree numbers whose product is not squarefree.
%C Squarefree numbers b(m) = A005117(m) such that gcd(b(m),b(m+1)) > 1. - _Thomas Ordowski_, Aug 15 2015
%H Robert Israel, <a href="/A077395/b077395.txt">Table of n, a(n) for n = 1..10000</a>
%F Conjecture: lim_{n->oo} n/a(n) > 0. - _Thomas Ordowski_ and _Robert Israel_, Aug 18 2015
%e A005117(106)*A005117(107) = 174*177 = (2*3*29)*(3*59) is not squarefree, therefore 174 is a term.
%p SF:= select(numtheory:-issqrfree,[$1..10000]):
%p map(t -> if igcd(SF[t],SF[t+1])>1 then SF[t] else NULL fi, [$1..nops(SF)-1]); # _Robert Israel_, Aug 16 2015
%t Transpose[Select[Partition[Select[Range[5000],SquareFreeQ],2,1], !SquareFreeQ[ Times@@#]&]][[1]] (* _Harvey P. Dale_, Dec 14 2012 *)
%o (PARI) lista(nn) = {last = 2; for (n=3, nn, if (issquarefree(n), if (! issquarefree(last*n), print1(last, ", ")); last = n;););} \\ _Michel Marcus_, Aug 17 2015
%Y Cf. A076144.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Nov 04 2002