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%I M5420 #53 Apr 11 2024 04:01:13
%S 242,3655,4503,5943,6853,7256,8392,9367,10983,11605,11606,12565,12855,
%T 12856,12872,13255,13782,13783,14312,16133,17095,18469,19045,19142,
%U 19143,19940,20165,20965,21368,21494,21495,21512,22855,23989,26885
%N Numbers k such that k, k+1, k+2 and k+3 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 Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 242, p. 67, Ellipses, Paris 2008.
%D Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B18, pp. 111-113.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Amiram Eldar, <a href="/A006601/b006601.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].
%H Victor Meally, <a href="/A006556/a006556.pdf">Letter to N. J. A. Sloane</a>, no date.
%t f[n_]:=Length[Divisors[n]]; lst={};Do[If[f[n]==f[n+1]==f[n+2]==f[n+3],AppendTo[lst,n]],{n,8!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 14 2009 *)
%t dsQ[n_]:=Length[Union[DivisorSigma[0,Range[n,n+3]]]]==1; Select[Range[ 30000],dsQ] (* _Harvey P. Dale_, Nov 23 2011 *)
%t Flatten[Position[Partition[DivisorSigma[0,Range[27000]],4,1],_?(Union[ Differences[ #]]=={0}&),{1},Heads->False]] (* Faster, because the number of divisors for each number is only calculated once *) (* _Harvey P. Dale_, Nov 06 2013 *)
%t SequencePosition[DivisorSigma[0,Range[27000]],{x_,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 a006601 n = a006601_list !! (n-1)
%o a006601_list = map (+ 1) $ elemIndices 0 $
%o zipWith3 (((+) .) . (+)) ds (tail ds) (drop 2 ds) where
%o ds = map abs $ zipWith (-) (tail a000005_list) a000005_list
%o -- _Reinhard Zumkeller_, Jan 18 2014
%o (PARI) is(n)=my(t=numdiv(n)); numdiv(n+1)==t && numdiv(n+2)==t && numdiv(n+3)==t \\ _Charles R Greathouse IV_, Jun 25 2017
%Y Cf. A000005, A006558, A019273, A119479.
%Y Other runs of equidivisor numbers: A005237 (runs of 2), A005238 (runs of 3), A049051 (runs of 5), A049052 (runs of 6), A049053 (runs of 7).
%K nonn,easy,nice,changed
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Olivier Gérard_
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