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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 Table of n, a(n) for n=1..70. 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 A361165 A358024 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 July 25 04:49 EDT 2024. Contains 374586 sequences. (Running on oeis4.)