A076136 Numbers n such that Omega(n) = Omega(n-1) + Omega(n-2), where Omega(n) (A001222) denotes the number of prime factors of n, counting multiplicity.

3, 4, 8, 12, 16, 36, 40, 54, 63, 75, 88, 104, 112, 132, 135, 140, 150, 195, 200, 204, 208, 220, 252, 279, 280, 294, 328, 375, 390, 399, 405, 408, 416, 423, 444, 456, 464, 486, 510, 516, 520, 525, 558, 560, 592, 612, 615, 616, 620, 630, 636, 644, 656, 663, 680

Offset: 1

Author

Joseph L. Pe, Oct 30 2002

Keywords

• nonn

Examples

			E.g. Omega(3) = 1 + 0 = Omega(2) + Omega(1). Omega(4) = 1 + 1 = Omega(3) + Omega(2).
8 is a term because Omega(8)=3=Omega(7)+Omega(6)=1+2=3
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A076137, A001222.

Programs

Mathematica

Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; l = {3}; Do[If[Omega[n] == Omega[n - 1] + Omega[n - 2], l = Append[l, n]], {n, 4, 1000}]; l
Flatten[Position[Partition[PrimeOmega[Range[700]],3,1],?(#[[1]]+#[[2]]==#[[3]]&),1,Heads->False]]+2 (* _Harvey P. Dale, Aug 24 2019 *)

PARI

j=[]; for(n=1,1000,if(bigomega(n)==bigomega(n-1)+bigomega(n-2),j=concat(j,n))); j