A068597 Barriers for bigomega(n): numbers n such that, for all m < n, m + bigomega(m) <= n.

2, 3, 4, 6, 8, 12, 24, 48, 60, 108, 168, 264, 348, 360, 384, 480, 720, 864, 888, 1020, 1320, 1440, 2040, 2064, 2448, 2880, 3024, 3120, 3168, 3624, 4680, 4920, 5388, 5400, 5880, 6600, 6720, 6984, 7080, 7560, 8424, 8700, 8784, 9744, 9840, 9888, 10080

Offset: 1

Author

Naohiro Nomoto, Mar 28 2002

Keywords

• nonn

References

• R. K. Guy, Unsolved Problems in Number Theory, B8.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Paul Erdos, Some Unconventional Problems in Number Theory, Mathematics Magazine, Vol. 52, No. 2, Mar., 1979, pp. 67-70. See Problem 4. p. 68.
• Paul Erdos, Some unconventional problems in number theory, Acta Mathematica Hungarica, 33(1):71-80, 1979.

Crossrefs

Cf. A005236.

Programs

Mathematica

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 *)

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