A345309 Numbers whose digital sum coincides with digital sum of their largest proper divisor.

18, 27, 36, 54, 72, 81, 90, 108, 126, 135, 144, 162, 180, 198, 216, 234, 243, 252, 270, 297, 306, 324, 342, 351, 360, 361, 378, 396, 405, 414, 432, 450, 504, 513, 522, 540, 551, 558, 567, 576, 594, 612, 621, 630, 702, 703, 720, 738, 756, 774, 792, 810, 837

Offset: 1

Author

Tanya Khovanova, Jun 13 2021

Keywords

• nonn
• base

Comments

Many of the numbers are multiples of 9. The ones that are not form sequence A219340.

Examples

			The largest proper divisor of 54 is 27. The sum of digits of 54 and 27 are the same. Thus 54 is in this sequence.
The largest proper divisor of 63 is 21. The sum of digits of 63 and 21 are not the same. Thus 63 is not in this sequence.
		

Crossrefs

Cf. A219340.

Programs

Mathematica

Select[Range[2, 10000], Total[IntegerDigits[#]] == Total[IntegerDigits[Divisors[#][[-2]]]] &]

Python

from sympy import divisors
def sd(n): return sum(map(int, str(n)))
def ok(n): return sd(n) == sd(divisors(n)[-2])
print(list(filter(ok, range(2, 840)))) # Michael S. Branicky, Jun 13 2021