A385640 Numbers k such that the sum of the digits of k divides k and the sum of the digits of k^2 divides k^2.

1, 2, 3, 6, 9, 10, 12, 18, 20, 21, 24, 30, 36, 42, 45, 48, 54, 60, 63, 72, 80, 84, 90, 100, 102, 108, 110, 111, 112, 117, 120, 126, 132, 140, 144, 150, 156, 162, 180, 190, 198, 200, 201, 204, 207, 210, 216, 220, 234, 240, 243, 252, 264, 270, 288, 300, 306, 315

Offset: 1

Author

Vighnesh Patil, Jul 05 2025

Keywords

• nonn
• base
• easy

Comments

If k is in the sequence then so is 10*k. - David A. Corneth, Jul 06 2025

Examples

			18 is a term since 1+8 = 9 and 18 mod 9 = 0; also, 18^2 = 324, and 3+2+4 = 9 and 324 mod 9 = 0.
		

Links

• Vighnesh Patil, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A005349 and A385656.

Cf. A007953.

Programs

Mathematica

A385640Q[k_] :=  Divisible[k, DigitSum[k]] && Divisible[k^2, DigitSum[k^2]];
Select[Range[500], A385640Q] (* Paolo Xausa, Jul 06 2025 *)

Python

def digit_sum(n): return sum(int(d) for d in str(n))
def ok(n):
    return n % digit_sum(n) == 0 and (n**2) % digit_sum(n**2) == 0
print([n for n in range(1, 400) if ok(n)])

Formula

A005349(a(n)) | a(n) and A005349(a(n)^2) | a(n)^2.

{k | k in A005349 and k^2 in A005349}. - Michael S. Branicky, Jul 05 2025