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

%I A069872 #31 Feb 18 2024 08:19:52
%S A069872 1,2,4,5,6,8,10,15,16,20,24,25,30,32,40,50,60,64,80,90,96,100,104,120,
%T A069872 124,125,128,150,160,200,240,250,255,256,288,320,360,375,380,384,400,
%U A069872 425,464,480,495,500,512,600,618,625,640,750,795,800,864,875,960,1000
%N A069872 Numbers k such that k divides the concatenation all divisors in ascending order, i.e., k divides A037278(k).
%C A069872 All the powers of 2 are terms.
%H A069872 Giovanni Resta, <a href="/A069872/b069872.txt">Table of n, a(n) for n = 1..1547</a> (terms <= 10^10, first 500 terms from Harvey P. Dale)
%e A069872 16 is a term as 16 divides 124816, 24 is a term as 24 divides 1234681224.
%t A069872 Select[Range[1000],Divisible[FromDigits[Flatten[IntegerDigits/@ Divisors[ #]]],#]&] (* _Harvey P. Dale_, Dec 31 2012 *)
%o A069872 (PARI) f(n) = my(d=divisors(n), s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ A037278
%o A069872 isok(n) = f(n) % n == 0; \\ _Michel Marcus_, Jun 01 2019
%o A069872 (Magma) k:=1; sol:=[];
%o A069872 for u in [1..1000] do D:=Divisors(u); conc:=D[1];
%o A069872     for u1 in [2..#D] do a:=#Intseq(conc); a1:=#Intseq(D[u1]);conc:=10^a1*conc+D[u1];end for;
%o A069872      if conc mod u eq 0 then sol[k]:=u; k:=k+1; end if;
%o A069872 end for;
%o A069872 sol; // _Marius A. Burtea_, Jun 01 2019
%Y A069872 Cf. A037278, A224930.
%K A069872 base,nonn
%O A069872 1,2
%A A069872 _Amarnath Murthy_, Apr 24 2002
%E A069872 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 21 2003