A219340 -id:A219340 - cp's OEIS frontend

A230354 Even numbers n such that digit sum of n = digit sum of largest odd divisor of n.

12, 18, 36, 54, 60, 72, 90, 108, 126, 132, 144, 156, 162, 180, 198, 204, 216, 228, 234, 240, 252, 270, 276, 306, 320, 324, 342, 348, 360, 372, 378, 396, 414, 420, 432, 450, 504, 516, 522, 540, 558, 594, 612, 624, 630, 636, 660, 702, 708, 720, 732, 738, 756, 774, 780, 792, 810, 900

Offset: 1

Antonio Roldán, Oct 16 2013

			Largest odd divisor of 162 is 81. Digit_sum(162)=9, digit_sum(81)=9

Cf. A006753, A219340, A230355, A230356, A230357.

mdi(n)= n / 2^valuation(n, 2)
digsum(n)={local (d, p); d=0; p=n; while(p, d+=p%10; p=floor(p/10)); return(d)}
{for (n=2, 10^3,m=mdi(n);if(digsum(n)==digsum(mdi(n))&&m<>n,print(n)));}

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

Original entry on oeis.org

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

Tanya Khovanova, Jun 13 2021

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

			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.

Cf. A219340.

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

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

cp's OEIS Frontend

A230354 Even numbers n such that digit sum of n = digit sum of largest odd divisor of n.

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