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
Keywords
Examples
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.
Crossrefs
Programs
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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]