A069872 Numbers k such that k divides the concatenation all divisors in ascending order, i.e., k divides A037278(k).

1, 2, 4, 5, 6, 8, 10, 15, 16, 20, 24, 25, 30, 32, 40, 50, 60, 64, 80, 90, 96, 100, 104, 120, 124, 125, 128, 150, 160, 200, 240, 250, 255, 256, 288, 320, 360, 375, 380, 384, 400, 425, 464, 480, 495, 500, 512, 600, 618, 625, 640, 750, 795, 800, 864, 875, 960, 1000

Offset

1,2

Comments

All the powers of 2 are terms.

Links

Giovanni Resta, Table of n, a(n) for n = 1..1547 (terms <= 10^10, first 500 terms from Harvey P. Dale)

Example

16 is a term as 16 divides 124816, 24 is a term as 24 divides 1234681224.

Mathematica

Select[Range[1000], Divisible[FromDigits[Flatten[IntegerDigits/@ Divisors[ #]]], #]&] (* Harvey P. Dale, Dec 31 2012 *)

Prog

(PARI) f(n) = my(d=divisors(n), s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ A037278
isok(n) = f(n) % n == 0; \\ Michel Marcus, Jun 01 2019
(Magma) k:=1; sol:=[];
for u in [1..1000] 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 u eq 0 then sol[k]:=u; k:=k+1; end if;
end for;
sol; // Marius A. Burtea, Jun 01 2019

Crossrefs

Cf. A037278, A224930.

Sequence in context: A175416 A190854 A362942 * A216163 A371182 A093080

Adjacent sequences: A069869 A069870 A069871 * A069873 A069874 A069875

Keyword

base,nonn

Author

Amarnath Murthy, Apr 24 2002

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 21 2003

Status

approved