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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.
1
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
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
KEYWORD
nonn,base
AUTHOR
Bernard Schott, May 13 2019
STATUS
approved