A216686 Numbers n such that n appears in the partial sums of the m-almost primes, where m=bigomega(n).

1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 40, 41, 58, 64, 80, 128, 160, 185, 197, 219, 254, 256, 281, 320, 377, 512, 589, 640, 843, 917, 964, 1024, 1247, 1280, 1652, 1707, 1804, 1825, 2048, 2074, 2157, 2519, 2560, 2637, 2642, 2727, 2771, 3614, 3755, 3786, 4046, 4096, 4227

Offset: 1

Author

Gerasimov Sergey, Sep 13 2012

Keywords

• nonn
• easy

Comments

A013918 is a subsequence. - Zak Seidov, Sep 17 2012

Or: Numbers n equal to the sum of the first k numbers x having bigomega(x)=bigomega(n), for some k. - M. F. Hasler, Sep 23 2012

Examples

			2 is in the sequence because 2 appears in A007504.
4 is in the sequence because 4 appears in A062198.
5 is in the sequence because 5 appears in A007504.
6 is not in the sequence because 6 is not in A062198.
8 is in the sequence because 8 appears in A086062,
10 is in the sequence because 10 appears in A062198.
		

Crossrefs

Cf. A001222, A007504, A013918, A062198, A092190, A086052, A086062.

Programs

Maple

alm := proc(n,m) # n-th m-almost prime
    option remember;
    if n =1 then
        2^m ;
    else
        for a from procname(n-1,m)+1 do
            if numtheory[bigomega](a) = m then
                return a;
            end if;
        end do:
    end if;
end proc:
almP := proc(n,m) #n-th partial sum of the m-almost primes
    add(alm(i,m),i=1..n) ;
end proc:
isA216686 := proc(n) # is n in the sequence?
    local m ,k,ps;
    m := numtheory[bigomega](n) ;
    for k from 1 do
        ps := almP(k,m) ;
        if ps = n then
            return true;
        elif ps > n then
            return false;
        end  if;
    end do:
end proc:
for n from 1 to 4300 do
    if isA216686(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Sep 14 2012

PARI

is_A216686(n)={ my(m=bigomega(n),t); while(n>0, while(bigomega(t++)!=m,); n-=t); !n}  \\ - M. F. Hasler, Sep 23 2012

Extensions

Corrected by R. J. Mathar, Sep 14 2012