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

Author

Amarnath Murthy, Apr 24 2002

Keywords

• base
• nonn

Comments

All the powers of 2 are terms.

Examples

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

Links

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

Crossrefs

Cf. A037278, A224930.

Programs

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

Mathematica

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

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

Extensions

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