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

Author

Stan Wagon, Jan 19 2019

Keywords

• nonn

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

• 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.