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A006532
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Numbers n such that sum of divisors is a square.
(Formerly M3089)
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24
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1, 3, 22, 66, 70, 81, 94, 115, 119, 170, 210, 214, 217, 265, 282, 310, 322, 343, 345, 357, 364, 382, 385, 400, 472, 497, 510, 517, 527, 642, 651, 679, 710, 742, 745, 782, 795, 820, 862, 884, 889, 930, 935, 966, 970, 1004, 1029, 1066, 1080, 1092, 1146
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If a and b are in the sequence and relatively prime, then a*b is also in the sequence. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 12 2009]
Apart from a(2), all terms are composite. Bunyakovsky's conjecture implies that this sequence is infinite, since then (e.g.) there are infinitely many primes of the form p=3k^2-1, whence sigma(2p) = 3p+3 = 9n^2. [Charles R Greathouse IV, May 12, 2011]
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 8.
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 94, p. 33, Ellipses, Paris 2008.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wells, Curious and interesting numbers, Penguin Books, p. 111.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
Index entries for sequences related to sums of squares
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MAPLE
| for i from 1 to 1000 do if issqr(sigma(i)) then print(i); fi; od;
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MATHEMATICA
| Select[ Range[ 1150 ], IntegerQ[ Sqrt[ DivisorSigma[ 1, # ] ] ]& ]
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CROSSREFS
| Cf. A074385, A000203. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 12 2009]
Sequence in context: A104604 A139272 A159345 * A178492 A005288 A143166
Adjacent sequences: A006529 A006530 A006531 * A006533 A006534 A006535
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Additional reference from Felice Russo (frusso(AT)micron.com). More terms from Enoch Haga (Enokh(AT)comcast.net).
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