%I #22 Apr 14 2019 06:16:13

%S 0,0,0,5,0,7,0,9,10,11,0,21,0,15,16,27,0,30,0,33,22,23,0,50,26,27,28,

%T 45,0,61,0,51,34,35,36,85,0,39,40,77,0,83,0,69,64,47,0,110,50,78,52,

%U 81,0,105,56,105,58,59,0,152,0,63,88,119,66,127,0,105,70,127

%N a(n) is the sum of the noncentral divisors of n.

%C a(n) = 0 iff n is 1 or a prime (A008578).

%H Harvey P. Dale, <a href="/A323643/b323643.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A000203(n) - A207376(n).

%e For n = 12 the divisors of 12 are 1, 2, 3, 4, 6, 12. The central divisors of 12 are both 3 and 4, therefore the noncentral divisors are 1, 2, 6, 12, and the sum of them is 1 + 2 + 6 + 12 = 21, so a(12) = 21.

%e For n = 16 the divisors of 16 are 1, 2, 4, 8, 16. The central divisor of 16 is 4, therefore the noncentral divisors of 16 are 1, 2, 8, 16, and the sum of them is 1 + 2 + 8 + 16 = 27, so a(16) = 27.

%t sncd[n_]:=Module[{d=Divisors[n],len},len=Length[d];If[EvenQ[len],Total[ Drop[ d, {len/2,len/2+1}]],Total[Drop[d,{(len+1)/2}]]]]; Array[sncd,70] (* _Harvey P. Dale_, Apr 13 2019 *)

%Y Cf. A000203, A008578, A027750, A161840, A169695, A207375, A207376.

%K nonn,easy,look

%O 1,4

%A _Omar E. Pol_, Feb 25 2019