A339980 Coreful Zumkeller numbers (A339979) whose set of coreful divisors can be partitioned into two disjoint sets of equal sum in a single way.

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.

Links

Table of n, a(n) for n=1..47.

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.

Cf. A007947, A057723.

Similar sequences: A083209, A335143, A335199, A335202, A335217, A335219.

Sequence in context: A339979 A322657 A364930 * A347892 A066216 A355033

Adjacent sequences: A339977 A339978 A339979 * A339981 A339982 A339983

Keyword

nonn

Author

Amiram Eldar, Dec 25 2020

Status

approved