A323610 List of 5-powerful numbers (for the definition of k-powerful see A323395).

48, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 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

Offset

1,1

Comments

The sequence consists of the multiples of 8 that are greater than or equal to 64, together with 48. The result is due to D. Boyd, Berend, and Golan. It had been conjectured that the sequence began with 64, but Boyd discovered the set

{1,2,7,10,11,12,13,14,16,17,21,22,27,28,32,33,35,36,37,38,39,42,47,48},

which shows that 48 is 5-powerful.

Links

Table of n, a(n) for n=1..57.

D. Berend and S. Golan, Littlewood polynomials with high order zeros, Math. Comp. 75 (2006) 1541-1552.

D. Boyd, On a problem of Byrnes concerning polynomials with restricted coefficients, Math. Comp. 66 (1997) 1697-1703.

Stan Wagon, Overview Table

Crossrefs

Cf. A323395.

Sequence in context: A114821 A108098 A114505 * A186400 A205188 A333672

Adjacent sequences: A323607 A323608 A323609 * A323611 A323612 A323613

Keyword

nonn

Author

Stan Wagon, Jan 19 2019

Status

approved