A035133 Cubeful (i.e., not cubefree) palindromes.

8, 88, 232, 272, 343, 424, 464, 616, 656, 686, 696, 808, 848, 888, 999, 1331, 2112, 2552, 2662, 2992, 3773, 3993, 4224, 4664, 6336, 6776, 8008, 8448, 8888, 14641, 18981, 19791, 21112, 21312, 21512, 21712, 21912, 23032, 23232, 23432, 23632

Offset: 1

Author

Patrick De Geest, Nov 15 1998

Keywords

• nonn
• base

Comments

Chourasiya & Johnston show that there are infinitely many palindromes not in this sequence. - Charles R Greathouse IV, May 14 2025

Examples

			E.g., 34643 = 7^3 * 101.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..627 from R. J. Mathar)
• Shashi Chourasiya and Daniel R. Johnston, Power-free palindromes and reversed primes, arXiv preprint (2025). arXiv:2503.21136 [math.NT]
• Eric Weisstein's World of Mathematics, Cubefree.

Crossrefs

Cf. A002113, A004709, A035132, A046099.

Programs

Mathematica

Select[Range[25000],PalindromeQ[#]&&Max[FactorInteger[#][[;;,2]]]>2&] (* Harvey P. Dale, Feb 18 2024 *)

Formula

A046099 INTERSECT A002113. - R. J. Mathar, Dec 08 2015