A214154 Number of ways to represent 2n as the sum of two distinct k-almost primes: #{mA001222(m)=A001222(2n-m)}.

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, 7, 11, 18, 9, 11, 14, 14, 8, 18, 12, 12, 19, 11, 12, 21, 9, 18, 14, 16, 13, 21, 16, 19, 16, 17, 13, 34, 12, 15, 22, 20, 15, 23, 14, 17, 17, 22

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 05 2012

Keywords

• nonn

Comments

Number of ways to represent 2n as the sum of two distinct numbers with the same number of prime divisors (counted with multiplicity).

Examples

			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).
		

Crossrefs

Cf. A001222, A045917.

Programs

Maple

iskalmos := proc(n,k)
        numtheory[bigomega](n) = k ;
end proc:
sumDistKalmost := proc(n,k)
        a := 0 ;
        for i from 0 to n/2 do
                if iskalmos(i,k) and iskalmos(n-i,k) and i <> n-i then
                        a := a+1 ;
                end if;
        end do:
        return a;
end proc:
A214154 := proc(n)
        a := 0 ;
        for k from 1 do
                if 2^k > n then
                        break;
                end if;
                a := a+sumDistKalmost(2*n,k) ;
        end do:
        return a;
end proc: # R. J. Mathar, Jul 05 2012
A214154 := n->add(`if`(numtheory[bigomega](m)=numtheory[bigomega](2*n-m),1,0), m=2..n-1); # M. F. Hasler, Jul 21 2012

PARI

A214154(n)=sum(m=2,n-1,bigomega(m)==bigomega(2*n-m)) \\ - M. F. Hasler, Jul 21 2012