A345309 - OEIS

%I #16 Jun 14 2021 16:08:24

%S 18,27,36,54,72,81,90,108,126,135,144,162,180,198,216,234,243,252,270,

%T 297,306,324,342,351,360,361,378,396,405,414,432,450,504,513,522,540,

%U 551,558,567,576,594,612,621,630,702,703,720,738,756,774,792,810,837

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

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

%e 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.

%e 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.

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

%o (Python)

%o from sympy import divisors

%o def sd(n): return sum(map(int, str(n)))

%o def ok(n): return sd(n) == sd(divisors(n)[-2])

%o print(list(filter(ok, range(2, 840)))) # _Michael S. Branicky_, Jun 13 2021

%Y Cf. A219340.

%K nonn,base

%O 1,1

%A _Tanya Khovanova_, Jun 13 2021