A307703 Highly powerful numbers (A005934) that are not cubeful (A036966).

4, 144, 288, 86400, 129600, 194400, 259200, 518400, 190512000, 317520000, 381024000, 635040000, 9681819840000, 215982036990720000, 9466852651364908800000, 14200278977047363200000, 28400557954094726400000, 174294224164279335916800000, 522882672492838007750400000

Offset: 1

Author

Amiram Eldar, Apr 22 2019

Keywords

• nonn
• fini
• full

Comments

Lacampagne and Selfridge proved that these are the only terms.

The positions of the terms in A005934 are 2, 8, 10, 25, 27, 28, 30, 33, 55, 58, 60, 62, 107, 161, 230, 234, 240, 302, 315.

Links

• Carole B. Lacampagne and John L. Selfridge, Large highly powerful numbers are cubeful, Proceedings of the American Mathematical Society, Vol. 91, No. 2 (1984), pp. 173-181.

Crossrefs

Cf. A005934, A036966.

Programs

Mathematica

pmax = 1; s = {}; Do[e = FactorInteger[n][[;; , 2]]; p = Times @@ e; If[p > pmax, pmax = p; If[Min[e] < 3, AppendTo[s, n]]], {n, 2, 10^6}]; s