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

1,1

Comments

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

Links

Table of n, a(n) for n=1..53.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A219340.

Sequence in context: A109911 A239878 A065751 * A337752 A279108 A038632

Adjacent sequences: A345306 A345307 A345308 * A345310 A345311 A345312

Keyword

nonn,base

Author

Tanya Khovanova, Jun 13 2021

Status

approved