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 A076191 #31 Apr 11 2021 08:05:52 %S A076191 1,0,1,-1,1,-1,2,-1,0,-1,2,-2,1,0,2,-3,2,-2,2,-1,0,-1,3,-2,0,1,0,-2,2, %T A076191 -2,4,-3,0,0,2,-3,1,0,2,-3,2,-2,2,0,-1,-1,4,-3,1,-1,1,-2,3,-2,2,-2,0, %U A076191 -1,3,-3,1,1,3,-4,1,-2,2,-1,1,-2,4,-4,1,1,0,-1,1,-2,4,-1,-2,-1,3,-2,0,0,2,-3,3,-2,1,-1,0,0,4,-5,2,0,1,-3 %N A076191 First differences of A001222. %C A076191 a(A045920(n)) = 0. - _Reinhard Zumkeller_, Mar 19 2012 %H A076191 Reinhard Zumkeller, <a href="/A076191/b076191.txt">Table of n, a(n) for n = 1..10000</a> %F A076191 a(n) = Omega(n+1)-Omega(n), where Omega(n) (A001222) denotes the number of prime factors of n, counting multiplicity. %F A076191 G.f.: ((1 - x)/x)*Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)). - _Ilya Gutkovskiy_, Mar 15 2017 %t A076191 Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; Flatten[Append[{1}, Table[Omega[n + 1] - Omega[n], {n, 2, 100}]]] %o A076191 (Haskell) %o A076191 a076191 n = a076191_list !! (n-1) %o A076191 a076191_list = zipWith (-) (tail a001222_list) a001222_list %o A076191 -- _Reinhard Zumkeller_, Mar 20 2012 %o A076191 (PARI) a(n) = bigomega(n + 1) - bigomega(n); \\ _Indranil Ghosh_, Mar 15 2017 %Y A076191 Cf. A001222, A045920. %K A076191 easy,sign %O A076191 1,7 %A A076191 _Joseph L. Pe_, Nov 03 2002 %E A076191 Name changed by _Arkadiusz Wesolowski_, Jul 27 2012