A308105 Numbers m such that m is greater than the sum of the k-th powers of its digits, where k is the number of digits of m.

10, 11, 12, 13, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 80, 81, 82, 83, 84, 90, 91, 92, 93, 100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 130, 131, 132, 133, 134

Offset

1,1

Comments

These integers are called "nombres résistants" on the French site Diophante.

There exists a smallest number M_0 such that every number >= M_0 is a term of this sequence. This integer has 60 digits: M_0 = 102 * 10^57. So 102 * 10^57 - 1 is not "résistant" (proof in the link).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Diophante, A367. Les entiers font de la résistance, Oct. 2017 (in French).

Formula

Numbers m such that m - A101337(m) > 0.

Example

34 - (3^2 + 4^2) = 9 so 34 is a term.
126 - (1^3 + 2^3 + 6^3) = -99 and 126 is not a term.

Maple

filter:= proc(n) local L, m, t;
  L:= convert(n, base, 10);
  m:= nops(L);
  n > add(t^m, t=L)
end proc:
select(filter, [$1..1000]); # Robert Israel, Jun 21 2019

Mathematica

Select[Range[140], # - Total[IntegerDigits[#]^IntegerLength[#]] > 0 &] (* Michael De Vlieger, Jun 09 2019 *)

Prog

(Magma) sol:=[]; v:=[]; digit:=[]; m:=1;
for u in [1..150] do
        digit:=Intseq(u);
             for i in [1..#digit] do v[i]:=digit[i]^#digit; end for;
             if u-&+v gt 0 then sol[m]:=u; m:=m+1; end if;
end for;
sol; // Marius A. Burtea, May 13 2019
(PARI) isok(n) = { my(d=digits(n), nb=#d); n > sum(k=1, #d, d[k]^nb); } \\ Michel Marcus, May 19 2019

Crossrefs

Cf. A000027, A101337, A005188.

Sequence in context: A138582 A215059 A362264 * A066309 A244510 A107860

Adjacent sequences: A308102 A308103 A308104 * A308106 A308107 A308108

Keyword

nonn,base

Author

Bernard Schott, May 13 2019

Status

approved