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A258786 Numbers n whose sum of anti-divisors is a permutation of their digits.

%I A258786 #10 Jun 16 2015 14:19:56
%S A258786 5,8,41,56,64,358,614,946,1092,1382,1683,2430,2683,2734,2834,2945,
%T A258786 3045,3067,3602,4056,4286,5186,5784,6874,7251,8104,8546,9264,12881,
%U A258786 14028,14384,15258,17386,21103,22044,23331,24434,24603,25346,26420,26822,26845,27024,27232
%N A258786 Numbers n whose sum of anti-divisors is a permutation of their digits.
%C A258786 A073930 is a subset of this sequence.
%H A258786 Paolo P. Lava, <a href="/A258786/b258786.txt">Table of n, a(n) for n = 1..200</a>
%e A258786 Anti-divisors of 5 are 2, 3 whose sum is 5.
%e A258786 Anti-divisors of 41 are 2, 3, 9, 27 whose sum is 41.
%e A258786 Anti-divisors of 64 are 3, 43 whose sum is 46 that is a permutation of the digit of 64.
%p A258786 with(numtheory):P:=proc(q) local a,b,j,k,ok,n,p;
%p A258786 for n from 1 to q do k:=0; j:=n;
%p A258786 while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
%p A258786 a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
%p A258786 if ilog10(n)=ilog10(a) then j:=sort(convert(n,base,10)); a:=sort(convert(a,base,10)); ok:=1;
%p A258786 for k from 1 to nops(a) do if j[k]<>a[k] then ok:=0; break;
%p A258786 fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^9);
%t A258786 ad[n_] := Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; Select[Range@ 5000, SameQ[DigitCount@ #, DigitCount[Total[ad@ #]]] &] (* _Michael De Vlieger_, Jun 10 2015 *)
%o A258786 (Python)
%o A258786 from sympy.ntheory.factor_ import antidivisors
%o A258786 A258786_list = [n for n in range(1,10**5) if sorted(str(n)) == sorted(str(sum(antidivisors(n))))] # _Chai Wah Wu_, Jun 11 2015
%Y A258786 Cf. A066417, A073930, A114065, A115920, A115921, A175795, A225902.
%K A258786 nonn,base
%O A258786 1,1
%A A258786 _Paolo P. Lava_, Jun 10 2015