cp's OEIS Frontend

A214154 Number of ways to represent 2n as the sum of two distinct k-almost primes: #{m A001222(m)=A001222(2n-m)}.

%I A214154 #13 Jul 22 2012 09:29:47
%S A214154 0,0,0,1,2,1,2,3,3,4,2,5,4,4,6,5,4,8,4,8,7,6,5,12,8,7,8,8,7,15,6,13,9,
%T A214154 7,11,18,9,11,14,14,8,18,12,12,19,11,12,21,9,18,14,16,13,21,16,19,16,
%U A214154 17,13,34,12,15,22,20,15,23,14,17,17,22
%N A214154 Number of ways to represent 2n as the sum of two distinct k-almost primes: #{m<n | A001222(m)=A001222(2n-m)}.
%C A214154 Number of ways to represent 2n as the sum of two distinct numbers with the same number of prime divisors (counted with multiplicity).
%e A214154 a(10)=4 because 2*10 = 3(1-almost prime) + 17(1-almost prime) = 6(2-almost prime) + 14(2-almost prime) = 7(1-almost prime) + 13(1-almost prime) = 8(3-almost prime) + 12(3-almost prime).
%p A214154 iskalmos := proc(n,k)
%p A214154         numtheory[bigomega](n) = k ;
%p A214154 end proc:
%p A214154 sumDistKalmost := proc(n,k)
%p A214154         a := 0 ;
%p A214154         for i from 0 to n/2 do
%p A214154                 if iskalmos(i,k) and iskalmos(n-i,k) and i <> n-i then
%p A214154                         a := a+1 ;
%p A214154                 end if;
%p A214154         end do:
%p A214154         return a;
%p A214154 end proc:
%p A214154 A214154 := proc(n)
%p A214154         a := 0 ;
%p A214154         for k from 1 do
%p A214154                 if 2^k > n then
%p A214154                         break;
%p A214154                 end if;
%p A214154                 a := a+sumDistKalmost(2*n,k) ;
%p A214154         end do:
%p A214154         return a;
%p A214154 end proc: # _R. J. Mathar_, Jul 05 2012
%p A214154 A214154 := n->add(`if`(numtheory[bigomega](m)=numtheory[bigomega](2*n-m),1,0), m=2..n-1); # _M. F. Hasler_, Jul 21 2012
%o A214154 (PARI) A214154(n)=sum(m=2,n-1,bigomega(m)==bigomega(2*n-m)) \\ - _M. F. Hasler_, Jul 21 2012
%Y A214154 Cf. A001222, A045917.
%K A214154 nonn
%O A214154 1,5
%A A214154 _Juri-Stepan Gerasimov_, Jul 05 2012