A200927 Difference between (least semiprime >= n) and (largest semiprime <= n).

0, 2, 0, 3, 3, 0, 0, 4, 4, 4, 0, 0, 6, 6, 6, 6, 6, 0, 0, 3, 3, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 3, 3, 0, 0, 7, 7, 7, 7, 7, 7, 0, 3, 3, 0, 2, 0, 4, 4, 4, 0, 2, 0, 0, 4, 4, 4, 0, 3, 3, 0, 4, 4, 4, 0, 5, 5, 5, 5, 0, 3, 3, 0, 5, 5, 5, 5, 0, 3, 3, 0, 0, 0, 4, 4, 4

Offset: 4

Author

Arkadiusz Wesolowski, Nov 24 2011

Keywords

• nonn

Comments

a(n) = 0 if and only if n is semiprime.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 4..10000

Crossrefs

Cf. A001358, A065516.

Programs

Maple

A106325 := proc(n)
    for a from n do
        if numtheory[bigomega](a) = 2 then
            return a;
        end if;
    end do:
end proc;
prevSpr := proc(n)
    for a from n by -1 do
        if numtheory[bigomega](a) = 2 then
            return a;
        end if;
    end do:
end proc;
A200927 := proc(n)
    A106325(n)-prevSpr(n) ;
end proc:
seq(A200927(n),n=4..80) ; # R. J. Mathar, Nov 26 2011

Mathematica

Table[a = b = 0; While[! PrimeOmega[n - a] == 2, a++]; While[! PrimeOmega[n + b] == 2, b++]; a + b, {n, 4, 100}]