

A323629


List of 6powerful numbers (for the definition of kpowerful see A323395).


2



96, 128, 144, 160, 176, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432, 440, 448, 456, 464, 472, 480, 488, 496, 504, 512, 520, 528, 536
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 6powerful.


REFERENCES

S. Golan, R. Pratt, S. Wagon, Equipowerful numbers, to appear.


LINKS

Table of n, a(n) for n=1..49.
G. Freiman and S. Litsyn, Asymptotically exact bounds on the size of highorder spectralnull codes, IEE Trans. Inform. Theory 45:6 (1999) 17981807.
Stan Wagon, Witnessing sets for the 6powerful numbers
Stan Wagon, Overview table


FORMULA

G.f.: 8*x*(x^6+2*x^2+8*x12)/(x1)^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 ith 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

Cf. A323614, A323610, A323395.
Sequence in context: A153484 A060660 A258748 * A146992 A261287 A252689
Adjacent sequences: A323625 A323626 A323627 * A323630 A323631 A323632


KEYWORD

nonn,easy


AUTHOR

Stan Wagon, Jan 20 2019


EXTENSIONS

More terms added by Stan Wagon, Jan 25 2019


STATUS

approved



