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 A006601 Numbers n such that n, n+1, n+2 and n+3 have the same number of divisors. (Formerly M5420) 13
 242, 3655, 4503, 5943, 6853, 7256, 8392, 9367, 10983, 11605, 11606, 12565, 12855, 12856, 12872, 13255, 13782, 13783, 14312, 16133, 17095, 18469, 19045, 19142, 19143, 19940, 20165, 20965, 21368, 21494, 21495, 21512, 22855, 23989, 26885 (list; graph; refs; listen; history; text; internal format)
 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 242, p. 67, 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 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]. Victor Meally, Letter to N. J. A. Sloane, no date. MAPLE with(numtheory);  A006601:=proc(q) local n; for n from 1 to q do   if tau(n)=tau(n+1) and tau(n+1)=tau(n+2) and tau(n+2)=tau(n+3) then print(n); fi; od; end: A006601(10^4); # Paolo P. Lava, May 03 2013 MATHEMATICA 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 *) dsQ[n_]:=Length[Union[DivisorSigma[0, Range[n, n+3]]]]==1; Select[Range[ 30000], dsQ] (* Harvey P. Dale, Nov 23 2011 *) 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 *) SequencePosition[DivisorSigma[0, Range[27000]], {x_, x_, x_, x_}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 03 2017 *) PROG (Haskell) import Data.List (elemIndices) a006601 n = a006601_list !! (n-1) a006601_list = map (+ 1) \$ elemIndices 0 \$    zipWith3 (((+) .) . (+)) ds (tail ds) (drop 2 ds) where    ds = map abs \$ zipWith (-) (tail a000005_list) a000005_list -- Reinhard Zumkeller, Jan 18 2014 (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 CROSSREFS Cf. A000005, A005237, A005238. Sequence in context: A160551 A258886 A165935 * A283723 A035748 A022153 Adjacent sequences:  A006598 A006599 A006600 * A006602 A006603 A006604 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Olivier Gérard STATUS approved

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Last modified August 18 12:29 EDT 2018. Contains 313832 sequences. (Running on oeis4.)