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A005238
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Numbers k such that k, k+1 and k+2 have the same number of divisors.
(Formerly M5236)
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28
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33, 85, 93, 141, 201, 213, 217, 230, 242, 243, 301, 374, 393, 445, 603, 633, 663, 697, 902, 921, 1041, 1105, 1137, 1261, 1274, 1309, 1334, 1345, 1401, 1641, 1761, 1832, 1837, 1885, 1893, 1924, 1941, 1981, 2013, 2054, 2101, 2133, 2181, 2217, 2264, 2305
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp. 12, Ellipses, Paris 2008.
R. K. Guy, Unsolved Problems in Number Theory, B18.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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MATHEMATICA
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Select[Range[2500], DivisorSigma[0, #]==DivisorSigma[0, #+1] == DivisorSigma[ 0, #+2]&] (* Harvey P. Dale, Nov 12 2012 *)
Flatten[Position[Partition[DivisorSigma[0, Range[2500]], 3, 1], {x_, x_, x_}]] (* Harvey P. Dale, Jul 06 2015 *)
SequencePosition[DivisorSigma[0, Range[2500]], {x_, x_, x_}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 03 2017 *)
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PROG
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(Haskell)
import Data.List (elemIndices)
a005238 n = a005238_list !! (n-1)
a005238_list = map (+ 1) $ elemIndices 0 $ zipWith (+) ds $ tail ds where
ds = map abs $ zipWith (-) (tail a000005_list) a000005_list
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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