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A172398 Number of partitions of n into the sum of two refactorable numbers (A033950). 4
0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 1, 2, 0, 1, 1, 0, 0, 3, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 1, 1, 1, 0, 2, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{i=1..floor(n/2)} ((1+floor(i/d(i)) - ceiling(i/d(i))) * (1 + floor((n-i)/d(n-i)) - ceiling((n-i)/d(n-i)))). - Wesley Ivan Hurt, Jan 12 2013

EXAMPLE

a(10)=2 because 10 = 1(refactorable) + 9(refactorable) = 2(refactorable) + 8(refactorable).

MAPLE

with(numtheory);

a:=n-> sum( ((1 + floor(i/tau(i)) - ceil(i/tau(i))) * (1 + floor((n-i)/tau(n-i)) - ceil((n-i)/tau(n-i))) ), i=1..floor(n/2));

# alternative

isA033950 := proc(n)

    if modp(n, numtheory[tau](n)) = 0 then

        true;

    else

        false;

    end if;

end proc:

A172398 := proc(n)

    local a;

    a := 0 ;

    for i from 1 to n/2 do

        if isA033950(i) and isA033950(n-i) then

            a := a+1 ;

        end if;

    end do:

    a ;

end proc: # R. J. Mathar, Jul 21 2015

CROSSREFS

Cf. A033950.

Sequence in context: A319020 A099200 A093578 * A070107 A299908 A044933

Adjacent sequences:  A172395 A172396 A172397 * A172399 A172400 A172401

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Nov 20 2010

EXTENSIONS

Corrected by D. S. McNeil, Nov 20 2010

STATUS

approved

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Last modified February 18 12:52 EST 2020. Contains 332018 sequences. (Running on oeis4.)