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

1,1

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

Table of n, a(n) for n=1..19.

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.

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

Crossrefs

Cf. A005934, A036966.

Sequence in context: A239248 A225133 A122422 * A277948 A083688 A053899

Adjacent sequences: A307700 A307701 A307702 * A307704 A307705 A307706

Keyword

nonn,fini,full

Author

Amiram Eldar, Apr 22 2019

Status

approved