A359074 Numbers that have at least two divisors with an equal sum of digits.

10, 12, 18, 20, 21, 22, 24, 27, 30, 36, 40, 42, 44, 45, 48, 50, 52, 54, 60, 63, 66, 70, 72, 80, 81, 84, 88, 90, 96, 100, 102, 104, 105, 108, 110, 111, 112, 114, 115, 117, 120, 124, 126, 130, 132, 133, 135, 136, 140, 144, 147, 150, 152, 153, 154, 156, 160, 162, 165

Offset

1,1

Comments

If k is a term, then so are all multiples of k. - Robert Israel, Dec 20 2022

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

24 is a term since it has two pairs of divisors having an equal sum of digits: 3 and 12; 6 and 24.

Maple

q:= n-> (s-> is(nops(s)>nops({s[]})))(map(x-> add(i, i=convert(x,
         base, 10)), [numtheory[divisors](n)[]])):
select(q, [$1..165])[];  # Alois P. Heinz, Dec 18 2022

Mathematica

a={}; For[k=1, k<=165, k++, If[Length[Intersection[Table[Total[Part[IntegerDigits[Divisors[k]], i]], {i, DivisorSigma[0, k]}]]] < DivisorSigma[0, k], AppendTo[a, k]]]; a
tdesQ[n_]:=AnyTrue[Tally[Total[IntegerDigits[#]]&/@Divisors[n]][[All, 2]], #>1&]; Select[ Range[200], tdesQ] (* Harvey P. Dale, Jan 13 2023 *)

Prog

(Python)
from sympy import divisors
def sod(n): return sum(map(int, str(n)))
def ok(n):
    s = set()
    for d in divisors(n, generator=True):
        sd = sod(d)
        if sd in s: return True
        s.add(sd)
    return False
print([k for k in range(166) if ok(k)]) # Michael S. Branicky, Dec 15 2022
(PARI) isok(k) = my(d=divisors(k)); #Set(apply(sumdigits, d)) < #d; \\ Michel Marcus, Dec 19 2022

Crossrefs

Complement of A359075.

Cf. A000005, A007953, A359076 (proper divisors).

Sequence in context: A031183 A265043 A158871 * A247626 A247627 A327709

Adjacent sequences: A359071 A359072 A359073 * A359075 A359076 A359077

Keyword

nonn,base

Author

Stefano Spezia, Dec 15 2022

Status

approved