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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 (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
Sequence in context: A081366 A129636 A242443 * A048219 A361165 A358024
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified July 25 04:49 EDT 2024. Contains 374586 sequences. (Running on oeis4.)