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