A309017 Numbers that divide the sum of the digits of their cubes.

1, 2, 3, 8, 9, 17, 18, 26, 27

Offset: 1

Author

Kritsada Moomuang, Jul 06 2019

Keywords

• nonn
• base
• full
• fini

Comments

There are no further terms since the cubes between 28 and 50 that have the highest sums of digits are 31, 46 and 49. The sum of digits of the cubes of 31, 46 and 49 are 28. 28 is not divisible by 31, 46 or 49. So it is impossible that any number greater than 50 can divide the sum of digits of its cube.

0 is not in the term because 0 divided by 0 is undefined.

Examples

			8 is in the sequence because 8^3 = 512 and 5 + 1 + 2 = 8, and 8/8 = 1.
		

Crossrefs

Cf. A000578 (n^3), A004164 (sum of digits of n^3).

Programs

Mathematica

Select[Range[1000], Divisible[Plus@@IntegerDigits[#^3], #] &] (* Alonso del Arte, Jul 07 2019 *)

PARI

isok(n) = !(sumdigits(n^3) % n); \\ Michel Marcus, Jul 07 2019