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A339980
Coreful Zumkeller numbers (A339979) whose set of coreful divisors can be partitioned into two disjoint sets of equal sum in a single way.
0
36, 72, 180, 200, 252, 360, 392, 396, 468, 504, 600, 612, 684, 784, 792, 828, 936, 1044, 1116, 1176, 1224, 1260, 1332, 1368, 1400, 1476, 1548, 1656, 1692, 1908, 1936, 1960, 1980, 2088, 2124, 2196, 2200, 2232, 2340, 2352, 2412, 2520, 2556, 2600, 2628, 2664, 2704
OFFSET
1,1
COMMENTS
A coreful divisor d of a number k is a divisor with the same set of distinct prime factors as k, or rad(d) = rad(k), where rad(k) is the largest squarefree divisor of k (A007947).
The coreful perfect numbers (A307958) are a subsequence.
EXAMPLE
36 is a term since there is only one partition of its set of coreful divisors, {6, 12, 18, 36}, into 2 disjoint sets whose sums are equal: 6 + 12 + 18 = 36.
MATHEMATICA
corZumQ[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]] == 2]; Select[Range[10000], corZumQ]
CROSSREFS
A307958 is a subsequence.
Subsequence of A308053 and A339979.
Similar sequences: A083209, A335143, A335199, A335202, A335217, A335219.
Sequence in context: A339979 A322657 A364930 * A347892 A066216 A355033
KEYWORD
nonn
AUTHOR
Amiram Eldar, Dec 25 2020
STATUS
approved