OFFSET
1,1
COMMENTS
EXAMPLE
48 is a term since it is not exponentially odd number (48 = 2^4 * 3 and 4 is even), and its set of bi-unitary divisors, {1, 2, 3, 6, 8, 16, 24, 48}, can be partitioned into 2 disjoint sets, whose sum is equal: 1 + 2 + 3 + 8 + 16 + 24 = 6 + 48.
MATHEMATICA
uDivs[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &]; bDivs[n_] := Select[Divisors[n], Last @ Intersection[uDivs[#], uDivs[n/#]] == 1 &]; bzQ[n_] := Module[{d = bDivs[n], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]]; expOddQ[n_] := AllTrue[Last /@ FactorInteger[n], OddQ]; Select[Range[1000], !expOddQ[#] && bzQ[#] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 27 2020
STATUS
approved