login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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 A087188 A102885

Adjacent sequences:  A214151 A214152 A214153 * A214155 A214156 A214157

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Jul 05 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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