A076156 Numbers n such that Omega(n+1) = Omega(n)+1, where Omega(m) (A001222) denotes the number of prime factors of m, counting multiplicity.

1, 3, 5, 13, 26, 37, 49, 51, 61, 62, 65, 69, 73, 74, 77, 91, 99, 115, 123, 125, 129, 146, 157, 169, 185, 187, 188, 193, 194, 195, 206, 221, 231, 235, 237, 254, 265, 267, 274, 275, 277, 278, 289, 291, 309, 313, 321, 343, 355, 362, 363, 365, 374, 386, 397, 398

Offset: 1

Author

Joseph L. Pe, Nov 01 2002

Keywords

• easy
• nonn

Comments

A079890(a(n)) = a(n)+1. - Reinhard Zumkeller, Feb 01 2008

Examples

			Omega(26 + 1) = 3 = 1 + 2 = 1 + Omega(26), so 26 is a term of the sequence.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Reinhard Zumkeller).

Programs

Mathematica

Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; l = {1}; Do[ If[Omega[i + 1] == Omega[i] + 1, l = Append[l, i]], {i, 2, 10^3}]; l
Position[Partition[PrimeOmega[Range[400]],2,1],?(#[[1]]+1==#[[2]]&), 1, Heads->False]//Flatten (* _Harvey P. Dale, May 15 2018 *)

Formula

a(n) seems to be asymptotic to c*n where c=7.6.... - Benoit Cloitre, Jan 15 2003