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A060355
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Numbers n such that n and n+1 are a pair of consecutive powerful numbers.
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6
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8, 288, 675, 9800, 12167, 235224, 332928, 465124, 1825200, 11309768, 384199200, 592192224, 4931691075, 5425069447, 13051463048, 221322261600, 443365544448, 865363202000, 8192480787000, 11968683934831, 13325427460800, 15061377048200, 28821995554247
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| "Erdos conjectured in 1975 that there do not exist three consecutive powerful integers." - Guy
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.
See Guy for Erdos' conjecture and statement that this sequence is infinite. - Jud McCranie , Oct 13 2002
It is easy to see that this sequence is infinite: if n is in the sequence, so is 4*n*(n+1). [From Franklin T. Adams-Watters, Sep 16 2009]
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REFERENCES
| J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 288, pp 74, Ellipses, Paris 2008.
R. K. Guy, Unsolved Problems in Number Theory, B16
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LINKS
| Donovan Johnson, Table of n, a(n) for n = 1..39 (terms < 10^22)
C. K. Caldwell, Powerful Numbers
Eric Weisstein's World of Mathematics, Powerful numbers
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MATHEMATICA
| f[n_]:=First[Union[Last/@FactorInteger[n]]]; Select[Range[2000000], f[#]>1&&f[#+1]>1&] (* From Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)
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CROSSREFS
| Cf. A001694, A060859, A199801.
Sequence in context: A079929 A136364 A089670 * A060859 A187289 A187191
Adjacent sequences: A060352 A060353 A060354 * A060356 A060357 A060358
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KEYWORD
| nonn,changed
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Apr 01 2001
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EXTENSIONS
| Corrected and extended by Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Jul 08 2001
More terms from Jud McCranie (JudMcCr(AT)BellSouth.net), Oct 13 2002
a(22)-a(23) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jul 29 2011
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