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 A214154 Number of ways to represent 2n as the sum of two distinct k-almost primes: #{m

%I

%S 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 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 17,13,34,12,15,22,20,15,23,14,17,17,22

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

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

%e 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 iskalmos := proc(n,k)

%p numtheory[bigomega](n) = k ;

%p end proc:

%p sumDistKalmost := proc(n,k)

%p a := 0 ;

%p for i from 0 to n/2 do

%p if iskalmos(i,k) and iskalmos(n-i,k) and i <> n-i then

%p a := a+1 ;

%p end if;

%p end do:

%p return a;

%p end proc:

%p A214154 := proc(n)

%p a := 0 ;

%p for k from 1 do

%p if 2^k > n then

%p break;

%p end if;

%p a := a+sumDistKalmost(2*n,k) ;

%p end do:

%p return a;

%p end proc: # _R. J. Mathar_, Jul 05 2012

%p 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 (PARI) A214154(n)=sum(m=2,n-1,bigomega(m)==bigomega(2*n-m)) \\ - _M. F. Hasler_, Jul 21 2012

%Y Cf. A001222, A045917.

%K nonn

%O 1,5

%A _Juri-Stepan Gerasimov_, Jul 05 2012

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Last modified June 13 05:41 EDT 2021. Contains 344981 sequences. (Running on oeis4.)