A339983 Coreful abundant numbers (A308053) with an even sum of coreful divisors (A057723) that are not coreful Zumkeller numbers (A339979).

108, 216, 432, 540, 756, 864, 972, 1000, 1080, 1188, 1404, 1512, 1728, 1836, 1944, 2000, 2052, 2160, 2376, 2484, 2744, 2808, 3000, 3024, 3132, 3348, 3456, 3672, 3780, 3888, 3996, 4000, 4104, 4320, 4428, 4644, 4752, 4860, 4968, 5076, 5488, 5616, 5724, 5940, 6000

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Example

108 is a term since its set of coreful divisors, {6, 12, 18, 36, 54, 108}, has an even sum, 234 > 2*108, and it cannot be partitioned into two disjoint sets of equal sum.

Mathematica

q[n_] := Module[{r = Times @@ FactorInteger[n][[;; , 1]], d, sum, x}, d = r*Divisors[n/r]; (sum = Plus @@ d) >= 2*n && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] == 0]; Select[Range[10^4], q]

Crossrefs

Subsequence of A308053.

Cf. A057723, A339979, A339982.

Similar sequences: A171641, A323341, A323342, A323343, A323344.

Sequence in context: A044340 A044721 A095050 * A275996 A235292 A202202

Adjacent sequences: A339980 A339981 A339982 * A339984 A339985 A339986

Keyword

nonn

Author

Amiram Eldar, Dec 25 2020

Status

approved