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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

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OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

CROSSREFS

Sequence in context: A026720 A026003 A103792 * A339984 A141630 A289467

Adjacent sequences: A076153 A076154 A076155 * A076157 A076158 A076159

KEYWORD

easy,nonn

AUTHOR

Joseph L. Pe, Nov 01 2002

STATUS

approved