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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A076137, A001222.

Sequence in context: A357501 A085635 A077434 * A064188 A229990 A353188

Adjacent sequences: A076133 A076134 A076135 * A076137 A076138 A076139

Keyword

nonn

Author

Joseph L. Pe, Oct 30 2002

Status

approved