OFFSET
1,1
COMMENTS
Any term of A335218 is of the form k*m where k is a term of this sequence and m is a squarefree number coprime to k. Therefore, A335218 can be generated from this sequence by multiplying terms with coprime squarefree numbers, and the asymptotic density of A335218 can be evaluated from the terms of this sequence (see the Comments section of A335218).
The least odd term is a(1715) = A321147(1) = 225450225 = (3 * 5 * 7 * 11 * 13)^2, which is the least odd exponential abundant number.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..11902 (terms below 10^10)
EXAMPLE
36 = 2^2 * 3^2 is a term since it is a powerful number, and its exponential divisors, {6, 12, 18, 36}, can be partitioned into 2 disjoint sets whose sum is equal: 6 + 12 + 18 = 36. By multiplying 36 by any squarefree number that is coprime to 36 we get another exponential Zumkeller number. E.g., 36 * 5 = 180 is an exponential Zumkeller number since its exponential divisors, {6*5, 12*5, 18*5, 36*5} = {30, 60, 90, 180}, can be partitioned into 2 disjoint sets whose sum is equal: 30 + 60 + 90 = 180.
MATHEMATICA
pows[max_] := Union[Flatten[Table[i^2*j^3, {j, 1, Surd[max, 3]}, {i, 1, Sqrt[max/j^3]}]]];
seq[max_] := Select[pows[max], ezQ]; seq[200000] (* using the function "ezQ" from A328136 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 28 2025
STATUS
approved