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A005238
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Numbers n such that n, n+1 and n+2 have the same number of divisors.
(Formerly M5236)
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21
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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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T. D. Noe, Table of n, a(n) for n = 1..1000
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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MAPLE
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with(numtheory); A005238:=proc(q) local n;
for n from 1 to q do
if tau(n)=tau(n+1) and tau(n+1)=tau(n+2) then print(n); fi;
od; end: A005238(10^4); # Paolo P. Lava, May 03 2013
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MATHEMATICA
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f[n_]:=Length[Divisors[n]]; lst={}; Do[If[f[n]==f[n+1]==f[n+2], AppendTo[lst, n]], {n, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)
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
-- Reinhard Zumkeller, Oct 03 2012
(PARI) is(n)=my(d=numdiv(n)); numdiv(n+1)==d && numdiv(n+2)==d \\ Charles R Greathouse IV, Feb 06 2017
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CROSSREFS
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Cf. A000005, A005237, A006601, A049051, A006558, A019273, A039665, A051950.
Sequence in context: A045939 A056809 A073251 * A052214 A063838 A075039
Adjacent sequences: A005235 A005236 A005237 * A005239 A005240 A005241
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Olivier Gérard
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STATUS
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approved
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