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 A045920 Numbers n such that factorizations of n and n+1 have the same number of primes (including multiplicities). 26
 2, 9, 14, 21, 25, 27, 33, 34, 38, 44, 57, 75, 85, 86, 93, 94, 98, 116, 118, 121, 122, 124, 133, 135, 141, 142, 145, 147, 153, 158, 164, 170, 171, 174, 177, 201, 202, 205, 213, 214, 217, 218, 230, 244, 245, 253, 284, 285, 296, 298, 301, 302, 326, 332, 334, 350, 356, 361 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A115186 is a subsequence: A001222(A115186(n))=A001222(A115186(n)+1)=n. - Reinhard Zumkeller, Jan 16 2006 Indices k such that A076191(k) = 0. - Ray Chandler, Dec 10 2008 A045939 is a subsequence. - Zak Seidov, Jul 02 2020 This sequence is infinite (Heath-Brown, 1984). - Amiram Eldar, Jul 11 2020 REFERENCES C. Clawson, Mathematical mysteries, Plenum Press 1996, p. 250 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 D. R. Heath-Brown, A parity problem from sieve theory, Mathematika, Vol. 29, No. 1 (1982), pp. 1-6. D. R. Heath-Brown, The divisor function at consecutive integers, Mathematika, Vol. 31, No. 1 (1984), pp. 141-149. Adolf Hildebrand, The divisor function at consecutive integers, Pacific journal of mathematics, Vol. 129, No. 2 (1987), pp. 307-319. FORMULA a(n) = A278291(n) - 1. - Zak Seidov, Nov 17 2018 MATHEMATICA f[n_]:=Plus@@Last/@FactorInteger[n]; lst={}; Do[If[f[n]==f[n+1], AppendTo[lst, n]], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *) Transpose[Transpose[Select[Partition[Table[{n, PrimeOmega[n]}, {n, 400}], 2, 1], #[[1, 2]]==#[[2, 2]]&]][[1]]][[1]] (* Harvey P. Dale, Feb 21 2012 *) Position[Differences[PrimeOmega[Range[400]]], 0] // Flatten (* Zak Seidov, Oct 30 2012 *) PROG (Haskell) import Data.List (elemIndices) a045920 n = a045920_list !! (n-1) a045920_list = map (+ 1) \$ elemIndices 0 a076191_list -- Reinhard Zumkeller, Mar 23 2012, Oct 11 2011 (PARI) is(n)=bigomega(n)==bigomega(n+1) \\ Charles R Greathouse IV, Sep 14 2015 CROSSREFS Sequence in context: A274133 A288483 A304807 * A242466 A071344 A224855 Adjacent sequences:  A045917 A045918 A045919 * A045921 A045922 A045923 KEYWORD nice,nonn AUTHOR EXTENSIONS More terms from David W. Wilson STATUS approved

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Last modified June 22 13:46 EDT 2021. Contains 345380 sequences. (Running on oeis4.)