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A339983 Coreful abundant numbers (A308053) with an even sum of coreful divisors (A057723) that are not coreful Zumkeller numbers (A339979). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 01:46 EST 2021. Contains 349558 sequences. (Running on oeis4.)