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A337932
Number of ways to write n as the sum of two deficient numbers (A005100).
1
0, 1, 1, 2, 2, 3, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 6, 8, 6, 7, 6, 7, 7, 9, 7, 9, 8, 9, 8, 11, 8, 10, 9, 11, 10, 13, 10, 12, 11, 13, 11, 15, 11, 13, 12, 15, 13, 18, 13, 15, 14, 17, 15, 20, 15, 17, 15, 18, 16, 22, 16, 19, 17, 20, 18, 24, 18, 22, 19, 22, 19, 25, 19, 22, 20, 25, 21, 28
OFFSET
1,4
LINKS
FORMULA
a(n) = Sum_{i=1..floor(n/2)} c(i) * c(n-i), where c is the characteristic function of deficient numbers (A294934).
EXAMPLE
The deficient numbers start: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, ... .
a(5) = 2; 5 = 4+1 = 3+2 and 1,2,3,4 are all deficient numbers.
a(6) = 3; 6 = 5+1 = 4+2 = 3+3 and 1,2,3,4,5 are all deficient.
a(7) = 2; 7 = 5+2 = 4+3. Since 6 is not a deficient number, the sum 6+1 is not counted.
MAPLE
N:= 100: # for a(1)..a(N)
S:= select(t -> numtheory:-sigma(t) < 2*t, [$1..N]):
V:= Vector(N): V[S]:= 1:
R:= Vector(N):
for i in select(`<=`, S, N/2) do
R[2*i..N]:= R[2*i..N] + V[i..N-i]
od:
convert(R, list); # Robert Israel, Oct 09 2020
MATHEMATICA
Table[Sum[(1 - Sign[Floor[DivisorSigma[1, n - i]/(2 (n - i))]])*(1 - Sign[Floor[DivisorSigma[1, i]/(2 i)]]), {i, Floor[n/2]}], {n, 100}]
CROSSREFS
Sequence in context: A108309 A341307 A103469 * A029326 A239500 A029204
KEYWORD
nonn,look
AUTHOR
Wesley Ivan Hurt, Oct 01 2020
STATUS
approved