cp's OEIS Frontend

A090061 Numbers k divisible by exactly two nontrivial permutations (rearrangements) of the digits of k, excluding all permutations that result in digit loss.

%I A090061 #20 Jul 14 2025 10:11:51
%S A090061 571428,867132,874125,923076,5179428,5714028,5714280,5714820,5719428,
%T A090061 5971428,8524710,8571042,8671320,8679132,8741250,8749125,8914752,
%U A090061 8957142,9230760,9239076,37451268,41957028,42195708,42713568,42915780,42971580,43157286,43751286,48713562,51374268
%N A090061 Numbers k divisible by exactly two nontrivial permutations (rearrangements) of the digits of k, excluding all permutations that result in digit loss.
%C A090061 Trivial permutations are identified as those where the permutation = k itself. Digit loss occurs when a permutation has 0 in the most significant position, which drops off, leaving a number with fewer digits. For example, when k is 3105, the permutation 0315 is excluded because 315 has fewer digits than 3105.
%C A090061 In the first million values of k, there is only one term that is divisible by three lossless nontrivial permutations. That term is 857142 which is divisible by 142857, 285714 and 428571. Note that 857142 is equal to floor((6/7)*10^6).
%H A090061 David A. Corneth, <a href="/A090061/b090061.txt">Table of n, a(n) for n = 1..18986</a> (terms <= 10^10)
%H A090061 David A. Corneth, <a href="/A090061/a090061.gp.txt">PARI program</a>
%H A090061 Chuck Seggelin, <a href="https://web.archive.org/web/20040109232550/http://www.plastereddragon.com/maths/asortdiv.htm">Numbers Divisible by Digit Permutations</a>.
%e A090061 a(4)=923076 is a term because 923076 is divisible by both 230769 and 307692, two nontrivial permutations of 923076 with the same number of digits.
%o A090061 (PARI) \\ See Corneth link
%Y A090061 Cf. A090056, A090057.
%K A090061 nonn,base
%O A090061 1,1
%A A090061 _Chuck Seggelin_, Nov 21 2003
%E A090061 a(5)-a(25) from _Donovan Johnson_, Sep 16 2009
%E A090061 More terms from _David A. Corneth_, Jun 08 2025