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A172398 Number of partitions of n into the sum of two refactorable numbers (A033950). 5
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
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
MATHEMATICA
a[n_] := IntegerPartitions[n, {2}, Select[Range[n], Divisible[#, DivisorSigma[0, #]]&]] // Length;
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 04 2023 *)
CROSSREFS
Cf. A033950.
Sequence in context: A099200 A358351 A093578 * A070107 A299908 A044933
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected by D. S. McNeil, Nov 20 2010
STATUS
approved

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Last modified February 23 02:31 EST 2024. Contains 370265 sequences. (Running on oeis4.)