OFFSET
1,1
COMMENTS
The set consists of 96, 128, 144, 160, 176, and all multiples of 8 that are greater than or equal to 192. The values 200, 216, 232, 248, 264, 280 are by Golan, Pratt, and Wagon; these are sufficient to give all further entries that are 8 (mod 16). Freiman and Litsyn proved that there is some M so that the list beyond M consists of all multiples of 8.
The linked file gives sets proving that all the given values are 6-powerful.
REFERENCES
S. Golan, R. Pratt, S. Wagon, Equipowerful numbers, to appear.
LINKS
G. Freiman and S. Litsyn, Asymptotically exact bounds on the size of high-order spectral-null codes, IEE Trans. Inform. Theory 45:6 (1999) 1798-1807.
Stan Wagon, Witnessing sets for the 6-powerful numbers
Stan Wagon, Overview table
Index entries for linear recurrences with constant coefficients, signature (2, -1).
FORMULA
G.f.: -8*x*(x^6+2*x^2+8*x-12)/(x-1)^2. - Alois P. Heinz, Jan 25 2019
EXAMPLE
a(1) = 96 because {1, 2, 7, 10, 11, 12, 13, 14, 16, 17, 21, 22, 27, 28, 32, 33, 35, 36, 37, 38, 39, 42, 47, 48, 51, 52, 53, 54, 56, 57, 63, 66, 67, 68, 71, 72, 73, 74, 77, 78, 79, 82, 88, 89, 91, 92, 93, 94} has the property that the sum of the i-th powers of this set equals the same for its complement in {1, 2, ..., 96}, for each i = 0, 1, 2, 3, 4, 5, 6.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stan Wagon, Jan 20 2019
EXTENSIONS
More terms added by Stan Wagon, Jan 25 2019
STATUS
approved