cp's OEIS Frontend

A224930 Numbers n such that n divides the concatenation of all divisors in descending order.

%I A224930 #43 Feb 14 2020 09:26:12
%S A224930 1,561,1703,2883,11623,14721,32431,205119,361767,826471901,3747204067,
%T A224930 17463443163,404345080971,573488405493,5623233497397
%N A224930 Numbers n such that n divides the concatenation of all divisors in descending order.
%C A224930 Like A069872 but in descending order.
%C A224930 a(11) > 2*10^9. - _Donovan Johnson_, May 05 2013
%C A224930 a(16) > 10^13. - _Giovanni Resta_, Feb 14 2020
%e A224930 Divisors of 561 are 1, 3, 11, 17, 33, 51, 187, 561 and 5611875133171131 / 561 = 10003342483371.
%e A224930 Divisors of 1703 are 1, 13, 131, 1703 and 1703131131 / 1703 = 1000077.
%p A224930 with(numtheory); A224930:=proc(q) local a,b,c,d,f,k,n;
%p A224930 for n from 1 to q do a:=sort([op(divisors(n))]); b:=nops(a); c:=a[b];
%p A224930   for k from 1 to b-1 do d:=c; f:=0; while d>0 do f:=f+1; d:=trunc(d/10); od;
%p A224930   c:=c+a[k+1]*10^f; od; if type(c/n,integer) then print(n); fi;
%p A224930 od; end: A224930 (10^6); # _Paolo P. Lava_, May 02 2013
%t A224930 Select[Range[10^6/2]*2-1, Mod[ FromDigits@ Flatten@ IntegerDigits[ Reverse@ Divisors@ #], #] == 0 &] (* _Giovanni Resta_, May 05 2013 *)
%o A224930 (PARI) isok(k) = {my(s = "", d = Vecrev(divisors(k))); for (j=1, #d, s = concat(s, Str(d[j]));); eval(k) % k == 0;} \\ _Michel Marcus_, Feb 14 2020
%Y A224930 Cf. A069872.
%K A224930 nonn,base,more
%O A224930 1,2
%A A224930 _Paolo P. Lava_, May 02 2013
%E A224930 a(10) from _Donovan Johnson_, May 05 2013
%E A224930 a(11)-a(12) from _Giovanni Resta_, May 05 2013
%E A224930 a(13)-a(14) from _Giovanni Resta_, May 10 2013
%E A224930 a(15) from _Giovanni Resta_, Feb 14 2020