A359076 Numbers that have at least two proper divisors with an equal sum of digits.

20, 22, 24, 30, 36, 40, 42, 44, 48, 50, 52, 54, 60, 63, 66, 70, 72, 80, 81, 84, 88, 90, 96, 100, 102, 104, 105, 108, 110, 112, 115, 120, 124, 126, 130, 132, 135, 136, 140, 144, 147, 150, 154, 156, 160, 162, 165, 168, 170, 175, 176, 180, 189, 190, 192, 198, 200

Offset

1,1

Comments

If x is in A359074 then x*y is a term for all y >= 2. - Robert Israel, Jan 19 2023

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

q:= n-> (s-> is(nops(s)>nops({s[]})))(map(x-> add(i, i=convert(x,
         base, 10)), [(numtheory[divisors](n) minus {n})[]])):
select(q, [$1..200])[];  # Alois P. Heinz, Dec 18 2022

Mathematica

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

Prog

(PARI) isok(k) = my(d=setminus(Set(divisors(k)), [k])); #Set(apply(sumdigits, d)) < #d; \\ Michel Marcus, Dec 19 2022

Crossrefs

Complement of A359077.

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

Sequence in context: A095445 A094203 A095439 * A036227 A328636 A171953

Adjacent sequences: A359073 A359074 A359075 * A359077 A359078 A359079

Keyword

nonn,base

Author

Stefano Spezia, Dec 15 2022

Status

approved