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A005238
Numbers k such that k, k+1 and k+2 have the same number of divisors.
(Formerly M5236)
28
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
OFFSET
1,1
REFERENCES
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).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
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].
MATHEMATICA
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 *)
PROG
(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
KEYWORD
nonn,easy,nice
EXTENSIONS
More terms from Olivier Gérard
STATUS
approved

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