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

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

Offset

1,2

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.

Links

Table of n, a(n) for n=1..9.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A093765 A260020 A104577 * A247375 A282508 A103026

Adjacent sequences: A309014 A309015 A309016 * A309018 A309019 A309020

Keyword

nonn,base,full,fini

Author

Kritsada Moomuang, Jul 06 2019

Status

approved