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A076156
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Numbers n such that Omega(n+1) = Omega(n)+1, where Omega(m) (A001222) denotes the number of prime factors of m, counting multiplicity.
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6
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1, 3, 5, 13, 26, 37, 49, 51, 61, 62, 65, 69, 73, 74, 77, 91, 99, 115, 123, 125, 129, 146, 157, 169, 185, 187, 188, 193, 194, 195, 206, 221, 231, 235, 237, 254, 265, 267, 274, 275, 277, 278, 289, 291, 309, 313, 321, 343, 355, 362, 363, 365, 374, 386, 397, 398
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) seems to be asymptotic to c*n where c=7.6.... - Benoit Cloitre, Jan 15 2003
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EXAMPLE
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Omega(26 + 1) = 3 = 1 + 2 = 1 + Omega(26), so 26 is a term of the sequence.
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MATHEMATICA
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Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; l = {1}; Do[ If[Omega[i + 1] == Omega[i] + 1, l = Append[l, i]], {i, 2, 10^3}]; l
Position[Partition[PrimeOmega[Range[400]], 2, 1], _?(#[[1]]+1==#[[2]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, May 15 2018 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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