OFFSET
1,5
COMMENTS
Number of ways to represent 2n as the sum of two distinct numbers with the same number of prime divisors (counted with multiplicity).
EXAMPLE
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).
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
PROG
(PARI) A214154(n)=sum(m=2, n-1, bigomega(m)==bigomega(2*n-m)) \\ - M. F. Hasler, Jul 21 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Jul 05 2012
STATUS
approved