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Search: id:A056828
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| A056828 |
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Numbers that are not the sum of at most three powerful (1) numbers. |
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+0
4
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OFFSET
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1,1
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COMMENT
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Mollin and Walsh conjectured that there are no further terms.
Heath-Brown proved that the sequence is finite.
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REFERENCES
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Heath-Brown, D. R. "Ternary Quadratic Forms and Sums of Three Square-Full Numbers." In Seminaire de Theorie des Nombres, Paris 1986-87 (Ed. C. Goldstein). Boston, MA: Birkhauser, pp. 137-163, 1988.
Mollin and Walsh, On Powerful Numbers, Intern. J. Math. and Math. Sci, 9:801-806, 1986.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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Smallest powerful numbers are 1, 4, 8, 9, 16, 25,... so 7, 15 and 23 are not the sum of one, two or three of them.
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CROSSREFS
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Cf. A001694.
Sequence in context: A004771 A133655 A029724 this_sequence A113505 A076796 A056119
Adjacent sequences: A056825 A056826 A056827 this_sequence A056829 A056830 A056831
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KEYWORD
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fini,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Aug 30 2000
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EXTENSIONS
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No other terms less than 40000000 - Paul.Jobling(AT)WhiteCross.com, May 14, 2001.
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