A308486 Numbers such that the sum of divisors divides the concatenation (in ascending order) of divisors.

1, 2, 6, 10, 40, 98, 112, 120, 1904, 2680, 4040, 4128, 5136, 9920, 12224, 17900, 20880, 27800, 44160, 55520, 57121, 62240, 86866, 158880, 178120, 1431808, 1773920, 1825280, 1918640, 3751328, 5452288, 6749600, 7262120, 7446720, 9916832, 17777440, 46168000, 101829808

Offset

1,2

Comments

Numbers k such that A000203(k) divides A037278(k). - Michel Marcus, Jun 02 2019.

Similar to A308533 where anti-divisors are considered.

Links

Giovanni Resta, Table of n, a(n) for n = 1..50

Example

Divisors of 98 are 1, 2, 7, 14, 49, 98 and their sum is sigma(98) = 171. Then, 127144998 / 171 = 743538.

Maple

with(numtheory): P:=proc(q) local n; for n from 1 to q do if frac(parse(cat(op(sort([op(divisors(n))]))))/sigma(n))=0 then
print(n); fi; od; end: P(10^6);

Mathematica

Select[Range[10^6], Mod[FromDigits@ Flatten@ IntegerDigits[#], Total@ #] == 0 &@ Divisors@ # &] (* Michael De Vlieger, Jun 03 2019 *)

Prog

(Magma) k:=1; sol:=[];
for u in [1..10000000] do D:=Divisors(u); conc:=D[1];
    for u1 in [2..#D] do a:=#Intseq(conc); a1:=#Intseq(D[u1]); conc:=10^a1*conc+D[u1];
    end for;
      if conc mod SumOfDivisors(u) eq 0 then sol[k]:=u; k:=k+1; end if;
end for;
sol; // Marius A. Burtea, Jun 01 2019
(PARI) concd(n) = my(d=divisors(n), s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ A037278
isok(n) = (concd(n) % sigma(n)) == 0; \\ Michel Marcus, Jun 05 2019

Crossrefs

Cf. A000203, A037278, A069872, A224930, A240265, A308533.

Sequence in context: A258079 A027165 A111414 * A202533 A275700 A258899

Adjacent sequences: A308483 A308484 A308485 * A308487 A308488 A308489

Keyword

nonn,base

Author

Paolo P. Lava, May 31 2019

Extensions

a(30)-a(38) from Giovanni Resta, May 31 2019

Status

approved