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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.
13
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
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
Sequence in context: A357501 A085635 A077434 * A064188 A229990 A353188
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 30 2002
STATUS
approved