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A077617
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Numbers k such that Omega(k) = Omega(k+1) + Omega(k+2).
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1
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12, 16, 24, 40, 45, 48, 56, 84, 100, 105, 132, 136, 140, 165, 168, 189, 204, 210, 224, 228, 261, 264, 272, 297, 315, 330, 345, 357, 372, 378, 380, 405, 441, 444, 450, 464, 465, 468, 477, 496, 513, 520, 522, 525, 536, 544, 546, 561, 564, 567, 588, 608, 621
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OFFSET
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1,1
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COMMENTS
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Omega(n) denotes the number of prime factors of n, counting multiplicity.
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LINKS
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EXAMPLE
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a(2) = 16 is a term because Omega(16) = 4 = Omega(17) + Omega(18) = 1 + 3 = 4.
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MATHEMATICA
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Select[Range[1, 1000], PrimeOmega[#] == PrimeOmega[# + 1] + PrimeOmega[# + 2] &] (* Vaclav Kotesovec, Feb 13 2019 *)
Position[Partition[PrimeOmega[Range[700]], 3, 1], _?(#[[1]]==#[[2]]+#[[3]] &), 1, Heads->False]//Flatten (* Harvey P. Dale, Aug 18 2019 *)
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PROG
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(PARI) j=[]; for(n=1, 1000, if(bigomega(n)==bigomega(n+1)+bigomega(n+2), j=concat(j, n))); j
(Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [k:k in [2..650]| f(k) eq f(k+1)+ f(k+2)]; // Marius A. Burtea, Feb 19 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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