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URL: https://oeis.org/A214154

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A214154
Number of ways to represent 2n as the sum of two distinct k-almost primes: #{m<n | A001222(m)=A001222(2n-m)}.
3
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
1,5
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
# Alternative:
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
Sequence in context: A129636 A242443 A379381 * A048219 A361165 A358024
KEYWORD
nonn,changed
AUTHOR
STATUS
approved