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

1, 561, 1703, 2883, 11623, 14721, 32431, 205119, 361767, 826471901, 3747204067, 17463443163, 404345080971, 573488405493, 5623233497397

Offset: 1

Author

Paolo P. Lava, May 02 2013

Keywords

• nonn
• base
• more

Comments

Like A069872 but in descending order.

a(11) > 2*10^9. - Donovan Johnson, May 05 2013

a(16) > 10^13. - Giovanni Resta, Feb 14 2020

Examples

			Divisors of 561 are 1, 3, 11, 17, 33, 51, 187, 561 and 5611875133171131 / 561 = 10003342483371.
Divisors of 1703 are 1, 13, 131, 1703 and 1703131131 / 1703 = 1000077.
		

Crossrefs

Cf. A069872.

Programs

Maple

with(numtheory); A224930:=proc(q) local a,b,c,d,f,k,n;
for n from 1 to q do a:=sort([op(divisors(n))]); b:=nops(a); c:=a[b];
  for k from 1 to b-1 do d:=c; f:=0; while d>0 do f:=f+1; d:=trunc(d/10); od;
  c:=c+a[k+1]*10^f; od; if type(c/n,integer) then print(n); fi;
od; end: A224930 (10^6); # Paolo P. Lava, May 02 2013

Mathematica

Select[Range[10^6/2]*2-1, Mod[ FromDigits@ Flatten@ IntegerDigits[ Reverse@ Divisors@ #], #] == 0 &] (* Giovanni Resta, May 05 2013 *)

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

Extensions

a(10) from Donovan Johnson, May 05 2013

a(11)-a(12) from Giovanni Resta, May 05 2013

a(13)-a(14) from Giovanni Resta, May 10 2013

a(15) from Giovanni Resta, Feb 14 2020