Search: id:A068781
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%I A068781
%S A068781 8,24,27,44,48,49,63,75,80,98,99,116,120,124,125,135,147,152,168,171,
%T A068781 175,188,207,224,242,243,244,260,275,279,288,296,315,324,332,342,343,
%U A068781 350,351,360,363,368,375,387,404,423,424,440,459,475,476,495,507,512
%N A068781 Lesser of two consecutive numbers each divisible by a square.
%C A068781 Also numbers m such that mu(m)=mu(m+1)=0, where mu is the Moebius-function 
               (A008683); A081221(a(n))>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 10 2003
%C A068781 The sequence contains an infinite family of arithmetic progressions like 
               {36a+8}={8,44,80,116,152,188,...} ={4(9a+2)}. {36a+9} provides 2nd 
               non-square-free terms. Such AP's can be constructed to any term by 
               solution of a system of linear Diophantine equation. - Labos E. (labos(AT)ana.sote.hu), 
               Nov 25 2002
%C A068781 1. 4k^2 + 4k is a member for all k; i.e. 8 times a triangular number 
               is a member. 2. (4k+1) times an odd square - 1 is a member. 3. (4k+3) 
               times odd square is a member. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Apr 24 2003
%e A068781 44 is in the sequence because 44 = 2^2 * 11 and 45 = 3^2 * 5.
%t A068781 Select[ Range[2, 600], Max[ Transpose[ FactorInteger[ # ]] [[2]]] > 1 
               && Max[ Transpose[ FactorInteger[ # + 1]] [[2]]] > 1 &]
%Y A068781 Cf. A068780, A068140, A068781, A068782, A068783, A068784, A068785.
%Y A068781 Cf. A049535, A077647, A078143, A045882.
%Y A068781 Sequence in context: A029607 A060476 A048109 this_sequence A038524 A162829 
               A000118
%Y A068781 Adjacent sequences: A068778 A068779 A068780 this_sequence A068782 A068783 
               A068784
%K A068781 nonn
%O A068781 1,1
%A A068781 Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 04 2002

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