A383746 Numbers k such that k divides the sum of the digits of k^(3k).

1, 2, 3, 6, 9, 11, 18, 38, 43, 87, 126, 670, 1098, 2421, 3588, 4201, 5114, 5877, 5922, 6048, 11799, 46119, 46419, 55098, 55945, 77439, 91541, 129624, 153229, 182402

Offset: 1

Author

J.W.L. (Jan) Eerland, May 08 2025

Keywords

• nonn
• base
• hard
• more

Examples

			2 is a term since the sum of digits of 2^(3*2) is 64, which is divisible by 2.
3 is a term since the sum of digits of 3^(3*3) is 19683, which is divisible by 3.
1098 is a term since the sum of digits of 1098^(3*1098) is 45018, which is divisible by 1098.
		

Crossrefs

Cf. A083282, A108859.

Programs

Mathematica

Do[If[Mod[Plus @@ IntegerDigits[n^(3*n)], n] == 0, Print[n]], {n, 1, 10000}]

Python

from gmpy2 import digits, mpz
def ok(n): return n and sum(map(mpz, digits(n**(3*n))))%n == 0
print([k for k in range(1100) if ok(k)]) # Michael S. Branicky, May 08 2025

Extensions

a(21)-a(23) and a(28)-a(30) from Michael S. Branicky, May 08 2025