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
Keywords
Links
- Petr Kucheriaviy, On numbers not representable as n + ω(n), arXiv preprint (2022). arXiv:2203.12006 [math.NT]
Crossrefs
Cf. A337455.
Programs
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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.