A358973 Numbers of the form m + omega(m) with m a positive integer.

1, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 17, 18, 20, 22, 23, 24, 26, 28, 30, 32, 33, 35, 36, 37, 38, 40, 41, 42, 44, 45, 46, 47, 48, 50, 52, 53, 54, 56, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82

Offset: 1

Author

Charles R Greathouse IV, Dec 07 2022

Keywords

• nonn

Links

• Petr Kucheriaviy, On numbers not representable as n + ω(n), arXiv preprint (2022). arXiv:2203.12006 [math.NT]

Crossrefs

Cf. A337455.

Programs

PARI

list(lim)=my(v=List()); forfactored(n=1,lim\1-1, my(t=n[1]+omega(n)); if(t<=lim, listput(v,t))); Set(v)

Formula

Kucheriaviy proves that a(n) << n log log n and conjectures that a(n) ≍ n, that is, these numbers have positive lower density.