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%I #11 Oct 09 2020 12:08:20
%S 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,
%T 11,10,13,10,12,11,13,11,15,11,13,12,15,13,18,13,15,14,17,15,20,15,17,
%U 15,18,16,22,16,19,17,20,18,24,18,22,19,22,19,25,19,22,20,25,21,28
%N Number of ways to write n as the sum of two deficient numbers (A005100).
%H Robert Israel, <a href="/A337932/b337932.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{i=1..floor(n/2)} c(i) * c(n-i), where c is the characteristic function of deficient numbers (A294934).
%e The deficient numbers start: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, ... .
%e a(5) = 2; 5 = 4+1 = 3+2 and 1,2,3,4 are all deficient numbers.
%e a(6) = 3; 6 = 5+1 = 4+2 = 3+3 and 1,2,3,4,5 are all deficient.
%e a(7) = 2; 7 = 5+2 = 4+3. Since 6 is not a deficient number, the sum 6+1 is not counted.
%p N:= 100: # for a(1)..a(N)
%p S:= select(t -> numtheory:-sigma(t) < 2*t, [$1..N]):
%p V:= Vector(N): V[S]:= 1:
%p R:= Vector(N):
%p for i in select(`<=`,S,N/2) do
%p R[2*i..N]:= R[2*i..N] + V[i..N-i]
%p od:
%p convert(R,list); # _Robert Israel_, Oct 09 2020
%t 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}]
%Y Cf. A005100, A294934.
%K nonn,look
%O 1,4
%A _Wesley Ivan Hurt_, Oct 01 2020
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