A077617 Numbers k such that Omega(k) = Omega(k+1) + Omega(k+2).

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

Offset

1,1

Comments

Omega(n) denotes the number of prime factors of n, counting multiplicity.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(2) = 16 is a term because Omega(16) = 4 = Omega(17) + Omega(18) = 1 + 3 = 4.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A001222, A076136.

Sequence in context: A335244 A330546 A189763 * A182074 A192609 A157678

Adjacent sequences: A077614 A077615 A077616 * A077618 A077619 A077620

Keyword

nonn

Author

Shyam Sunder Gupta, Dec 01 2002

Status

approved