This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A045920 #49 Feb 11 2023 22:51:48
%S A045920 2,9,14,21,25,27,33,34,38,44,57,75,85,86,93,94,98,116,118,121,122,124,
%T A045920 133,135,141,142,145,147,153,158,164,170,171,174,177,201,202,205,213,
%U A045920 214,217,218,230,244,245,253,284,285,296,298,301,302,326,332,334,350,356,361
%N A045920 Numbers m such that the factorizations of m..m+1 have the same number of primes (including multiplicities).
%C A045920 A115186 is a subsequence: A001222(A115186(n)) = A001222(A115186(n)+1) = n. - _Reinhard Zumkeller_, Jan 16 2006
%C A045920 Indices k such that A076191(k) = 0. - _Ray Chandler_, Dec 10 2008
%C A045920 A045939 is a subsequence. - _Zak Seidov_, Jul 02 2020
%C A045920 This sequence is infinite (Heath-Brown, 1984). - _Amiram Eldar_, Jul 11 2020
%D A045920 C. Clawson, Mathematical mysteries, Plenum Press 1996, p. 250.
%H A045920 Reinhard Zumkeller, <a href="/A045920/b045920.txt">Table of n, a(n) for n = 1..10000</a>
%H A045920 D. R. Heath-Brown, <a href="https://doi.org/10.1112/S0025579300012109">A parity problem from sieve theory</a>, Mathematika, Vol. 29, No. 1 (1982), pp. 1-6.
%H A045920 D. R. Heath-Brown, <a href="https://doi.org/10.1112/S0025579300010743">The divisor function at consecutive integers</a>, Mathematika, Vol. 31, No. 1 (1984), pp. 141-149.
%H A045920 Adolf Hildebrand, <a href="https://projecteuclid.org/euclid.pjm/1102690578">The divisor function at consecutive integers</a>, Pacific journal of mathematics, Vol. 129, No. 2 (1987), pp. 307-319.
%F A045920 a(n) = A278291(n) - 1. - _Zak Seidov_, Nov 17 2018
%t A045920 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 *)
%t A045920 Transpose[Transpose[Select[Partition[Table[{n,PrimeOmega[n]},{n,400}], 2,1], #[[1,2]]==#[[2,2]]&]][[1]]][[1]] (* _Harvey P. Dale_, Feb 21 2012 *)
%t A045920 Position[Differences[PrimeOmega[Range[400]]], 0] // Flatten (* _Zak Seidov_, Oct 30 2012 *)
%o A045920 (Haskell)
%o A045920 import Data.List (elemIndices)
%o A045920 a045920 n = a045920_list !! (n-1)
%o A045920 a045920_list = map (+ 1) $ elemIndices 0 a076191_list
%o A045920 -- _Reinhard Zumkeller_, Mar 23 2012, Oct 11 2011
%o A045920 (PARI) is(n)=bigomega(n)==bigomega(n+1) \\ _Charles R Greathouse IV_, Sep 14 2015
%Y A045920 Numbers m through m+k have the same number of prime divisors (with multiplicity): this sequence (k=1), A045939 (k=2), A045940 (k=3), A045941 (k=4), A045942 (k=5), A123103 (k=6), A123201 (k=7), A358017 (k=8), A358018 (k=9), A358019 (k=10).
%K A045920 nice,nonn
%O A045920 1,1
%A A045920 _Felice Russo_
%E A045920 More terms from _David W. Wilson_