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 A006049 Numbers n such that n and n+1 have the same number of distinct prime divisors. 27
 2, 3, 4, 7, 8, 14, 16, 20, 21, 31, 33, 34, 35, 38, 39, 44, 45, 50, 51, 54, 55, 56, 57, 62, 68, 74, 75, 76, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 111, 115, 116, 117, 118, 122, 123, 127, 133, 134, 135, 141, 142, 143, 144, 145, 146, 147, 152, 158, 159, 160, 161, 171, 175 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence is infinite, as proved by Schlage-Puchta who comments: "Buttkewitz found a non-computational proof, and the Goldston-Pintz-Yildirim-sieve yields more precise information". - Charles R Greathouse IV, Jan 09 2013 REFERENCES C. Clawson, Mathematical mysteries, Plenum Press 1996, p. 250. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from T. D. Noe) Jan-Christoph Schlage-Puchta, The equation ω(n)=ω(n+1), arXiv:1105.1621 [math.NT], 2011. FORMULA A001221(a(n)) = A001221(a(n)+1). - Reinhard Zumkeller, Jan 22 2013 MATHEMATICA f[n_] := Length@FactorInteger[n]; t = f /@ Range[175]; Flatten@Position[Rest[t] - Most[t], 0] (* Ray Chandler, Mar 27 2007 *) Select[Range[200], PrimeNu[#]==PrimeNu[#+1]&] (* Harvey P. Dale, May 09 2012 *) Flatten[Position[Partition[PrimeNu[Range[200]], 2, 1], _?(#[[1]]==#[[2]]&), {1}, Heads->False]] (* Harvey P. Dale, May 22 2015 *) SequencePosition[PrimeNu[Range[200]], {x_, x_}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 02 2019 *) PROG (PARI) is(n)=omega(n)==omega(n+1) \\ Charles R Greathouse IV, Jan 09 2013 (Haskell) import Data.List (elemIndices) a006049 n = a006049_list !! (n-1) a006049_list = map (+ 1) \$ elemIndices 0 \$    zipWith (-) (tail a001221_list) a001221_list -- Reinhard Zumkeller, Jan 22 2013 CROSSREFS Cf. A001221, A052215, A107800, A006073. Subsequence of A062974. Sequence in context: A057887 A202116 A215914 * A084541 A240690 A113050 Adjacent sequences:  A006046 A006047 A006048 * A006050 A006051 A006052 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Extended by Ray Chandler, Mar 27 2007 STATUS approved

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Last modified August 11 18:37 EDT 2020. Contains 336428 sequences. (Running on oeis4.)