A076251 Numbers m such that omega(m) = omega(m-1) + omega(m-2), where omega(m) is the number of distinct prime factors of m.

3, 6, 10, 18, 30, 33, 42, 60, 66, 84, 90, 102, 105, 110, 114, 126, 129, 130, 138, 150, 165, 168, 174, 180, 195, 198, 210, 228, 234, 252, 264, 270, 273, 285, 290, 294, 315, 318, 330, 345, 348, 354, 360, 385, 399, 402, 420, 434, 450, 462, 465, 468, 480, 504

Offset: 1

Author

Joseph L. Pe, Nov 04 2002

Keywords

• nonn

Examples

			omega(18) = 2 = 1 + 1 = omega(17) + omega(16), so 18 belongs to the sequence.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A076252, A076253.

Programs

Mathematica

omega[n_] := Length[FactorInteger[n]]; Select[Range[3, 10^3], omega[ # ] == omega[ # - 1] + omega[ # - 2] &]

PARI

lista(kmax) = {my(o1 = omega(1), o2 = omega(2), o3); for(k = 3, kmax, o3 = omega(k); if(o3 == o1 + o2, print1(k, ", ")); o1 = o2; o2 = o3);} \\ Amiram Eldar, Sep 18 2024