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A335219 Exponential Zumkeller numbers (A335218) whose set of exponential divisors can be partitioned into two disjoint sets of equal sum in a single way. 3
36, 180, 252, 396, 468, 612, 684, 828, 1044, 1116, 1260, 1332, 1476, 1548, 1692, 1800, 1908, 1980, 2124, 2196, 2340, 2412, 2556, 2628, 2700, 2772, 2844, 2988, 3060, 3204, 3276, 3420, 3492, 3636, 3708, 3852, 3924, 4068, 4140, 4284, 4572, 4716, 4788, 4900, 4932 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Differs from A054979 first at a(44), since 4900 is in this sequence but not in A054979. - R. J. Mathar, Jun 02 2020
LINKS
EXAMPLE
36 is a term since there is a single way in which its exponential divisors, {6, 12, 18, 36} can be partitioned into 2 disjoint sets whose sum is equal: 6 + 12 + 18 = 36.
MATHEMATICA
dQ[n_, m_] := (n > 0 && m > 0 && Divisible[n, m]); expDivQ[n_, d_] := Module[{ft = FactorInteger[n]}, And @@ MapThread[dQ, {ft[[;; , 2]], IntegerExponent[d, ft[[;; , 1]]]}]]; eDivs[n_] := Module[{d = Rest[Divisors[n]]}, Select[d, expDivQ[n, #] &]]; ezQ[n_] := Module[{d = eDivs[n], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] == 2]]; Select[Range[10^4], ezQ]
CROSSREFS
The exponential of A083209.
Subsequence of A335218.
Sequence in context: A335218 A321145 A054979 * A102949 A211733 A211744
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 27 2020
STATUS
approved

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Last modified April 22 22:30 EDT 2024. Contains 371906 sequences. (Running on oeis4.)