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Search: id:A008849
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| A008849 |
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Numbers n such that the sum of divisors of n^3 is a square. |
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+0
5
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| 1, 7, 751530, 4730879, 5260710, 33116153, 37200735, 187062910, 226141311, 259109835, 260405145, 370049418, 522409465, 836308083, 1105725765, 1309440370, 1343713507, 1582989177, 1609505430, 1813768845, 2590345926, 3039492538, 3656866255
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In 1657 Fermat challenged the world to find such numbers. [Dickson, Vol. 1, p. 54]
If n is a term and n is not divisible by 7, then 7*n is a term. - Don Dechman (dondechman_2000(AT)yahoo.com), Mar 26 2008
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 9.
L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 1, p. 54.
Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 92.
I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): I. Fermat's first challenge, Preprint, 2002.
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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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CROSSREFS
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Cf. A046872, A008850.
Sequence in context: A003835 A138878 A050938 this_sequence A076914 A076915 A076910
Adjacent sequences: A008846 A008847 A008848 this_sequence A008850 A008851 A008852
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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David W. Wilson (davidwwilson(AT)comcast.net) has supplied terms a(4) = 4730879 and beyond and verified completeness up to a(3) = 751530.
I. Kaplansky and W. Jagy have verified that there are no other terms below 3.8*10^9.
3656866255 added by Don Dechman, Mar 26 2008
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