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A076191
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First differences of A001222.
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6
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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, -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, -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
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OFFSET
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1,7
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COMMENTS
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LINKS
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FORMULA
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a(n) = Omega(n+1)-Omega(n), where Omega(n) (A001222) denotes the number of prime factors of n, counting multiplicity.
G.f.: ((1 - x)/x)*Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)). - Ilya Gutkovskiy, Mar 15 2017
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MATHEMATICA
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Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; Flatten[Append[{1}, Table[Omega[n + 1] - Omega[n], {n, 2, 100}]]]
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PROG
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(Haskell)
a076191 n = a076191_list !! (n-1)
a076191_list = zipWith (-) (tail a001222_list) a001222_list
(PARI) a(n) = bigomega(n + 1) - bigomega(n); \\ Indranil Ghosh, Mar 15 2017
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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