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 A214154 Number of ways to represent 2n as the sum of two distinct k-almost primes: #{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 (list; graph; refs; listen; history; text; internal format)
 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). LINKS 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 Cf. A001222, A045917. Sequence in context: A081366 A129636 A242443 * A048219 A087188 A102885 Adjacent sequences:  A214151 A214152 A214153 * A214155 A214156 A214157 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Jul 05 2012 STATUS approved

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Last modified May 9 11:51 EDT 2021. Contains 343740 sequences. (Running on oeis4.)