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

1,1

Comments

A073930 is a subset of this sequence.

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A280965 A151349 A298935 * A192272 A073930 A342021

Adjacent sequences: A258783 A258784 A258785 * A258787 A258788 A258789

Keyword

nonn,base

Author

Paolo P. Lava, Jun 10 2015

Status

approved