A323643 a(n) is the sum of the noncentral divisors of n.

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, 45, 0, 61, 0, 51, 34, 35, 36, 85, 0, 39, 40, 77, 0, 83, 0, 69, 64, 47, 0, 110, 50, 78, 52, 81, 0, 105, 56, 105, 58, 59, 0, 152, 0, 63, 88, 119, 66, 127, 0, 105, 70, 127

Offset: 1

Author

Omar E. Pol, Feb 25 2019

Keywords

• nonn
• easy
• look

Comments

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

Examples

			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.
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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

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 *)

Formula

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