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

1,4

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A271228 A281528 A201334 * A325966 A134828 A292899

Adjacent sequences: A323640 A323641 A323642 * A323644 A323645 A323646

Keyword

nonn,easy,look

Author

Omar E. Pol, Feb 25 2019

Status

approved