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Search: id:A060355
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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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+0
5
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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"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 (JudMcCr(AT)BellSouth.net), Oct 13 2002
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]
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REFERENCES
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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
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C. K. Caldwell, Powerful Numbers
Eric Weisstein's World of Mathematics, Powerful numbers
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CROSSREFS
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Cf. A001694, A060859.
Sequence in context: A079929 A136364 A089670 this_sequence A060859 A054607 A132592
Adjacent sequences: A060352 A060353 A060354 this_sequence A060356 A060357 A060358
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KEYWORD
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nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Apr 01 2001
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EXTENSIONS
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Corrected and extended by Jud McCranie (j.mccranie(AT)comcast.net), Jul 08 2001
More terms from Jud McCranie (JudMcCr(AT)BellSouth.net), Oct 13 2002
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