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A248211
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First differences of omega(n), the number of distinct prime factors function (A001221).
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1
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1, 0, 0, 0, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, -1, 1, 0, 0, -1, 1, -1, 1, -1, 1, -1, 2, -2, 0, 1, 0, 0, 0, -1, 1, 0, 0, -1, 2, -2, 1, 0, 0, -1, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, -1, 2, -2, 1, 0, -1, 1, 1, -2, 1, 0, 1, -2, 1, -1, 1, 0, 0, 0, 1, -2, 1
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OFFSET
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1,29
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COMMENTS
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First instance of abs(a(n)) > 2 is for n = 210. - Alonso del Arte, Oct 05 2014
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LINKS
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FORMULA
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G.f.: (1 - x)*Sum_{k>=1} x^(prime(k)-1)/(1 - x^prime(k)). - Ilya Gutkovskiy, Mar 15 2017
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MAPLE
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with(numtheory): A248211:=n->nops(factorset(n+1))-nops(factorset(n)): seq(A248211(n), n=1..100);
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MATHEMATICA
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Table[PrimeNu[n + 1] - PrimeNu[n], {n, 100}] (* Hurt *)
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PROG
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(PARI) a(n) = omega(n+1) - omega(n); \\ Michel Marcus, Dec 29 2022
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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