A359076 - OEIS

%I #19 Jan 20 2023 01:30:50

%S 20,22,24,30,36,40,42,44,48,50,52,54,60,63,66,70,72,80,81,84,88,90,96,

%T 100,102,104,105,108,110,112,115,120,124,126,130,132,135,136,140,144,

%U 147,150,154,156,160,162,165,168,170,175,176,180,189,190,192,198,200

%N Numbers that have at least two proper divisors with an equal sum of digits.

%C If x is in A359074 then x*y is a term for all y >= 2. - _Robert Israel_, Jan 19 2023

%H Robert Israel, <a href="/A359076/b359076.txt">Table of n, a(n) for n = 1..10000</a>

%e 24 is a term since its proper divisors 3 and 12 have an equal sum of digits.

%p q:= n-> (s-> is(nops(s)>nops({s[]})))(map(x-> add(i, i=convert(x,

%p          base, 10)), [(numtheory[divisors](n) minus {n})[]])):

%p select(q, [$1..200])[];  # _Alois P. Heinz_, Dec 18 2022

%t a={}; For[k=1, k<=210, k++, If[Length[Intersection[Table[Total[Part[IntegerDigits[Divisors[k]], i]], {i, DivisorSigma[0,k]-1}]]] < DivisorSigma[0, k]-1, AppendTo[a, k]]]; a

%o (PARI) isok(k) = my(d=setminus(Set(divisors(k)), [k])); #Set(apply(sumdigits, d)) < #d; \\ _Michel Marcus_, Dec 19 2022

%Y Complement of A359077.

%Y Cf. A000005, A007953, A359074 (all the divisors).

%K nonn,base

%O 1,1

%A _Stefano Spezia_, Dec 15 2022