cp's OEIS Frontend

A282755 Numbers k such that the set of all the decimal digits of k is the same as the set of all the decimal digits of the proper divisors of k.

%I A282755 #21 Sep 09 2017 23:28:15
%S A282755 11,125,1255,2510,11009,11099,11255,11379,12326,12955,14379,14397,
%T A282755 15033,15303,16325,17482,21109,25105,31007,31503,33011,35213,37127,
%U A282755 37921,41303,44011,49319,51367,53491,63013,69413,70319,71057,72013,72517,74341,77011,81767
%N A282755 Numbers k such that the set of all the decimal digits of k is the same as the set of all the decimal digits of the proper divisors of k.
%C A282755 The primes of the form (10^n - 1)/9 are terms (A004022).
%C A282755 A majority of numbers of the sequence are semiprimes (so with 3 proper divisors), except 11, 125, 2510, 16325, 21109, 72013, 126530, 132644, 163025, ... with the corresponding number of proper divisors 1, 3, 7, 5, 7, 7, 7, 5, 5, 5, 7, 7, ...
%C A282755 The even numbers of the sequence are rarer than the odd numbers: 2510, 12326, 17482, 105002, 123206, ...
%C A282755 All terms have a 1 in their decimal representation (A011531). - _Michel Marcus_, Feb 23 2017
%C A282755 The union of 11 and A237713. - _R. J. Mathar_, Mar 06 2017
%e A282755 16325 is in the sequence because the set of the digits is E = {1, 2, 3, 5, 6} and the proper divisors (or aliquot parts) of 16325 are 1, 5, 25, 653 and 3265 with the same set of digits.
%p A282755 with(numtheory):
%p A282755 for n from 1 to 200000 do:
%p A282755 z:=convert(n,base,10):n0:=nops(z):lst1:={op(z),z[n0]}:
%p A282755 x:=divisors(n):n1:=nops(x):lst:={}:
%p A282755   for m from 1 to n1-1 do:
%p A282755    y:=convert(x[m],base,10):n2:=nops(y):
%p A282755    lst2:={op(y),y[n2]}:lst:=lst union lst2
%p A282755    od:
%p A282755    if lst1=lst then
%p A282755    printf(`%d, `,n):
%p A282755    else
%p A282755   fi:
%p A282755 od:
%t A282755 Select[Range[10^5], Function[k, Union@ Flatten@ Map[IntegerDigits, Most@ Divisors@ k] == Union@ IntegerDigits@ k]] (* _Michael De Vlieger_, Feb 25 2017 *)
%Y A282755 Cf. A004022, A011531, A032741.
%Y A282755 A variant of A237713.
%K A282755 nonn,base
%O A282755 1,1
%A A282755 _Michel Lagneau_, Feb 21 2017