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%I M5420
%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 n such that n, n+1, n+2 and n+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 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 242, p. 67, 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 T. D. Noe, <a href="/A006601/b006601.txt">Table of n, a(n) for n=1..1000</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%p with(numtheory); A006601:=proc(q) local n;
%p for n from 1 to q do
%p if tau(n)=tau(n+1) and tau(n+1)=tau(n+2) and tau(n+2)=tau(n+3) then print(n); fi;
%p od; end: A006601(10^4); # _Paolo P. Lava_, May 03 2013
%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 [From _Vladimir Joseph Stephan Orlovsky_, Dec 14 2009]
%t dsQ[n_]:=Length[Union[DivisorSigma[0,Range[n,n+3]]]]==1; Select[Range[ 30000],dsQ] (* From Harvey P. Dale, Nov 23 2011 *)
%Y Cf. A000005, A005237, A005238.
%K nonn,easy,nice
%O 1,1
%A _N. J. A. Sloane_.
%E More terms from _Olivier Gérard_
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