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

5, 8, 41, 56, 64, 358, 614, 946, 1092, 1382, 1683, 2430, 2683, 2734, 2834, 2945, 3045, 3067, 3602, 4056, 4286, 5186, 5784, 6874, 7251, 8104, 8546, 9264, 12881, 14028, 14384, 15258, 17386, 21103, 22044, 23331, 24434, 24603, 25346, 26420, 26822, 26845, 27024, 27232

Offset: 1

Author

Paolo P. Lava, Jun 10 2015

Keywords

• nonn
• base

Comments

A073930 is a subset of this sequence.

Examples

			Anti-divisors of 5 are 2, 3 whose sum is 5.
Anti-divisors of 41 are 2, 3, 9, 27 whose sum is 41.
Anti-divisors of 64 are 3, 43 whose sum is 46 that is a permutation of the digit of 64.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A066417, A073930, A114065, A115920, A115921, A175795, A225902.

Programs

Maple

with(numtheory):P:=proc(q) local a,b,j,k,ok,n,p;
for n from 1 to q do k:=0; j:=n;
while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
if ilog10(n)=ilog10(a) then j:=sort(convert(n,base,10)); a:=sort(convert(a,base,10)); ok:=1;
for k from 1 to nops(a) do if j[k]<>a[k] then ok:=0; break;
fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^9);

Mathematica

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 *)

Python

from sympy.ntheory.factor_ import antidivisors
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