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%I #17 Feb 26 2024 22:43:49
%S 2,3,4,6,8,12,24,48,60,108,168,264,348,360,384,480,720,864,888,1020,
%T 1320,1440,2040,2064,2448,2880,3024,3120,3168,3624,4680,4920,5388,
%U 5400,5880,6600,6720,6984,7080,7560,8424,8700,8784,9744,9840,9888,10080
%N Barriers for bigomega(n): numbers n such that, for all m < n, m + bigomega(m) <= n.
%D R. K. Guy, Unsolved Problems in Number Theory, B8.
%H Charles R Greathouse IV, <a href="/A068597/b068597.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Erdos, <a href="https://www.jstor.org/stable/2689842">Some Unconventional Problems in Number Theory</a>, Mathematics Magazine, Vol. 52, No. 2, Mar., 1979, pp. 67-70. See Problem 4. p. 68.
%H Paul Erdos, <a href="https://users.renyi.hu/~p_erdos/1979-23.pdf">Some unconventional problems in number theory</a>, Acta Mathematica Hungarica, 33(1):71-80, 1979.
%t omegaBarrierQ[n_] := (For[m = 1, m < n, m++, If[m + PrimeOmega[m] > n, Return[False]]]; True); Select[Range[2, 1100], omegaBarrierQ] (* _Amiram Eldar_ after _Jean-François Alcover_ at A005236 *)
%o (PARI) is(n)=if(isprime(n-1) && isprime(n\2-1),for(k=3,log(n)\log(2),if(bigomega(n-k)>k,return(0)));1, n<5 && n>1) \\ _Charles R Greathouse IV_, Sep 20 2012
%Y Cf. A005236.
%K nonn
%O 1,1
%A _Naohiro Nomoto_, Mar 28 2002