%I A060355
%S A060355 8,288,675,9800,12167,235224,332928,465124,1825200,11309768,384199200,
%T A060355 592192224,4931691075,5425069447,13051463048,221322261600,443365544448,
%U A060355 865363202000,8192480787000,11968683934831,13325427460800
%N A060355 Numbers n such that n and n+1 are a pair of consecutive powerful numbers.
%C A060355 "Erdos conjectured in 1975 that there do not exist three consecutive 
               powerful integers." - Guy
%C A060355 1825200 belongs to the sequence because 1825200=2.2.2.2.3.3.3.5.5.13.13, 
               1825201=7.7.193.193=1351^2 and both are powerful numbers. - Labos 
               E. (labos(AT)ana.sote.hu), May 03 2001.
%C A060355 See Guy for Erdos' conjecture and statement that this sequence is infinite. 
               - Jud McCranie (JudMcCr(AT)BellSouth.net), Oct 13 2002
%C A060355 It is easy to see that this sequence is infinite: if n is in the sequence, 
               so is 4n(n+1). [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Sep 16 2009]
%D A060355 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 288, pp 74, Ellipses, 
               Paris 2008.
%D A060355 R. K. Guy, Unsolved Problems in Number Theory, B16
%H A060355 C. K. Caldwell, <a href="http://primes.utm.edu/glossary/page.php?sort=PowerfulNumber">
               Powerful Numbers</a>
%H A060355 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PowerfulNumber.html">Powerful numbers</a>
%Y A060355 Cf. A001694, A060859.
%Y A060355 Sequence in context: A079929 A136364 A089670 this_sequence A060859 A054607 
               A132592
%Y A060355 Adjacent sequences: A060352 A060353 A060354 this_sequence A060356 A060357 
               A060358
%K A060355 nonn
%O A060355 1,1
%A A060355 Jason Earls (zevi_35711(AT)yahoo.com), Apr 01 2001
%E A060355 Corrected and extended by Jud McCranie (j.mccranie(AT)comcast.net), Jul 
               08 2001
%E A060355 More terms from Jud McCranie (JudMcCr(AT)BellSouth.net), Oct 13 2002