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A323629 List of 6-powerful numbers (for the definition of k-powerful 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 6-powerful.

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 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

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

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

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Last modified July 19 08:23 EDT 2019. Contains 325155 sequences. (Running on oeis4.)