%I M5236 #51 Feb 19 2024 01:48:39
%S 33,85,93,141,201,213,217,230,242,243,301,374,393,445,603,633,663,697,
%T 902,921,1041,1105,1137,1261,1274,1309,1334,1345,1401,1641,1761,1832,
%U 1837,1885,1893,1924,1941,1981,2013,2054,2101,2133,2181,2217,2264,2305
%N Numbers k such that k, k+1 and k+2 have the same number of divisors.
%D 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.
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp. 12, Ellipses, Paris 2008.
%D R. K. Guy, Unsolved Problems in Number Theory, B18.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Amiram Eldar, <a href="/A005238/b005238.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%t Select[Range[2500],DivisorSigma[0,#]==DivisorSigma[0,#+1] == DivisorSigma[ 0,#+2]&] (* _Harvey P. Dale_, Nov 12 2012 *)
%t Flatten[Position[Partition[DivisorSigma[0,Range[2500]],3,1],{x_,x_,x_}]] (* _Harvey P. Dale_, Jul 06 2015 *)
%t SequencePosition[DivisorSigma[0,Range[2500]],{x_,x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 03 2017 *)
%o (Haskell)
%o import Data.List (elemIndices)
%o a005238 n = a005238_list !! (n-1)
%o a005238_list = map (+ 1) $ elemIndices 0 $ zipWith (+) ds $ tail ds where
%o ds = map abs $ zipWith (-) (tail a000005_list) a000005_list
%o -- _Reinhard Zumkeller_, Oct 03 2012
%o (PARI) is(n)=my(d=numdiv(n)); numdiv(n+1)==d && numdiv(n+2)==d \\ _Charles R Greathouse IV_, Feb 06 2017
%Y Cf. A000005, A005237, A006601, A049051, A006558, A019273, A039665, A051950.
%K nonn,easy,nice
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Olivier GĂ©rard_