OFFSET
1,2
COMMENTS
Numbers with two consecutive zeros are not considered, to avoid the case 0^0. Nevertheless, even if we consider 0^0=1 the results do not change (at least up to the last number I tested, that is m=10^8).
EXAMPLE
For 63 we have 6^3 + 3^6 = 945 and 945/63 = 15.
Obviously also with 36 we have 3^6 + 6^3 = 945 but 945/36 = 105/4.
For 6189068 we have: 6^8 + 0^6 + 9^0 + 8^9 + 1^8 + 6^1 + 8^6 = 136159496.
Finally 136159496/6189068 = 22.
MAPLE
with(numtheory): P:=proc(q) local a, b, k, ok, n; for n from 10 to q do a:=[]; b:=n;
while b>0 do a:=[op(a), b mod 10]; b:=trunc(b/10); od; b:=0; ok:=1; for k from 2 to nops(a)
do if a[k-1]=0 and a[k]=0 then ok:=0; break; else b:=b+a[k]^a[k-1]; fi; od;
if ok=1 then if type((b+a[1]^a[nops(a)])/n, integer) then print(n);
fi; fi; od; end: P(10^10);
MATHEMATICA
fQ[n_] := Block[{id = IntegerDigits@ n}, IntegerQ[ Total[ (id^RotateLeft@ id)]/n]]; k = 1; lst = {}; While[k < 1000000001, If[fQ@k, AppendTo[lst, k]; Print@ k]; k++]; lst (* Robert G. Wilson v, Jun 01 2014 *)
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Paolo P. Lava, May 29 2014
STATUS
approved