A335219 Exponential Zumkeller numbers (A335218) whose set of exponential divisors can be partitioned into two disjoint sets of equal sum in a single way.

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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.

Cf. A335143, A335199, A335202.

Sequence in context: A335218 A321145 A054979 * A102949 A211733 A211744

Adjacent sequences: A335216 A335217 A335218 * A335220 A335221 A335222

Keyword

nonn

Author

Amiram Eldar, May 27 2020

Status

approved