OFFSET
1,2
COMMENTS
If a(n) = m + A001222(m) then (a(n) - m) <= log(a(n))/log(2).
It appears that a(n)/n may converge to a constant around ~ 1.49.
LINKS
Petr Kucheriaviy, On numbers not representable as n + ω(n), arXiv preprint (2022). arXiv:2203.12006 [math.NT]
FORMULA
Kucheriaviy proves that a(n) << n log log n and conjectures that a(n) ≍ n, that is, these numbers have positive lower density. - Charles R Greathouse IV, Dec 07 2022
EXAMPLE
a(7) = 10 + A001222(10) = 10 + 2 = 12
MATHEMATICA
m = 100; Select[Union @ Table[n + PrimeOmega[n], {n, 1, m}], # <= m &] (* Amiram Eldar, Aug 28 2020 *)
PROG
(PARI) upto(limit)=Set(select(t->t<=limit, apply(m->m+bigomega(m), [1..limit]))) \\ Andrew Howroyd, Aug 27 2020
(PARI) list(lim)=my(v=List()); forfactored(n=1, lim\1-1, my(t=n[1]+bigomega(n)); if(t<=lim, listput(v, t))); Set(v) \\ Charles R Greathouse IV, Dec 07 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Nathan J. McDougall, Aug 27 2020
STATUS
approved