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A006049
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Numbers n such that n and n+1 have same number of distinct prime divisors.
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7
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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)
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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C. Clawson, Mathematical mysteries, Plenum Press 1996, p. 250.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..2500
Jan-Christoph Schlage-Puchta, The equation ω(n)=ω(n+1), 2011
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FORMULA
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A001221(a(n)) = A001221(a(n)+1). - Reinhard Zumkeller, Jan 22 2013
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MATHEMATICA
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f[n_] := Length@FactorInteger[n]; t = f /@ Range[175]; Flatten@Position[Rest[t] - Most[t], 0] (* Ray Chandler *)
Select[Range[200], PrimeNu[#]==PrimeNu[#+1]&] (* Harvey P. Dale, May 09 2012 *)
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PROG
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(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
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CROSSREFS
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Cf. A001221, A052215, A107800, A006073.
Subsequence of A062974.
Sequence in context: A057887 A202116 A215914 * A084541 A113050 A015927
Adjacent sequences: A006046 A006047 A006048 * A006050 A006051 A006052
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Extended by Ray Chandler, Mar 27 2007
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STATUS
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approved
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