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

%I A216686 #18 Oct 01 2012 06:50:55
%S A216686 1,2,4,5,8,10,16,17,20,32,40,41,58,64,80,128,160,185,197,219,254,256,
%T A216686 281,320,377,512,589,640,843,917,964,1024,1247,1280,1652,1707,1804,
%U A216686 1825,2048,2074,2157,2519,2560,2637,2642,2727,2771,3614,3755,3786,4046,4096,4227
%N A216686 Numbers n such that n appears in the partial sums of the m-almost primes, where m=bigomega(n).
%C A216686 A013918 is a subsequence. - _Zak Seidov_, Sep 17 2012
%C A216686 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
%e A216686 2 is in the sequence because 2 appears in A007504.
%e A216686 4 is in the sequence because 4 appears in A062198.
%e A216686 5 is in the sequence because 5 appears in A007504.
%e A216686 6 is not in the sequence because 6 is not in A062198.
%e A216686 8 is in the sequence because 8 appears in A086062,
%e A216686 10 is in the sequence because 10 appears in A062198.
%p A216686 alm := proc(n,m) # n-th m-almost prime
%p A216686     option remember;
%p A216686     if n =1 then
%p A216686         2^m ;
%p A216686     else
%p A216686         for a from procname(n-1,m)+1 do
%p A216686             if numtheory[bigomega](a) = m then
%p A216686                 return a;
%p A216686             end if;
%p A216686         end do:
%p A216686     end if;
%p A216686 end proc:
%p A216686 almP := proc(n,m) #n-th partial sum of the m-almost primes
%p A216686     add(alm(i,m),i=1..n) ;
%p A216686 end proc:
%p A216686 isA216686 := proc(n) # is n in the sequence?
%p A216686     local m ,k,ps;
%p A216686     m := numtheory[bigomega](n) ;
%p A216686     for k from 1 do
%p A216686         ps := almP(k,m) ;
%p A216686         if ps = n then
%p A216686             return true;
%p A216686         elif ps > n then
%p A216686             return false;
%p A216686         end  if;
%p A216686     end do:
%p A216686 end proc:
%p A216686 for n from 1 to 4300 do
%p A216686     if isA216686(n) then
%p A216686         printf("%d,",n) ;
%p A216686     end if;
%p A216686 end do: # _R. J. Mathar_, Sep 14 2012
%o A216686 (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
%Y A216686 Cf. A001222, A007504, A013918, A062198, A092190, A086052, A086062.
%K A216686 nonn,easy
%O A216686 1,2
%A A216686 _Gerasimov Sergey_, Sep 13 2012
%E A216686 Corrected by _R. J. Mathar_, Sep 14 2012