OFFSET
1,2
COMMENTS
Digitsum = (A007953).
The 'k's are 2, 2, 4, 3, 4, 5, 7, 12, 15, 16, 19, 21, 57, 37, 38, 79, 48, 63, 72, 119, 306, 397, 469, 472, 582, 613, 927, 1461, 2926, 3449, ..., . - Robert G. Wilson v, Jul 30 2015
EXAMPLE
Digitsum(9) is 9, digitsum(9^2) is 9. (9+9)/2 = 9. So 9 is in this sequence.
12^1 = 12, 12^2 = 144, 12^3 = 1728 and 12^4 = 20736. Digitsum(12) = 3, digitsum(144) = 9, digitsum(1728) = 18, digitsum(20736) = 18, (3+9+18+18)/4 = 12. So 12 is in this sequence.
MATHEMATICA
fQ[n_] := If[ IntegerQ@ Log10@ n, False, Block[{pwr = 2, s = Plus @@ IntegerDigits@ n}, While[s = s + Plus @@ IntegerDigits[n^pwr]; s < n*pwr, pwr++]; If[s == n*pwr, True, False]]]; k = 1; lst = {1}; While[k < 100001, If[fQ@ k, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Jul 30 2015 *)
PROG
(Python)
def sod(n):
....kk = 0
....while n > 0:
........kk= kk+(n%10)
........n =int(n//10)
....return kk
for c in range (2, 10**4):
....bb=0
....for a in range(1, 200):
........bb=bb+sod(c**a, 10)
........if bb==c*a:
............print (c, a)
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Pieter Post, Jun 24 2015
EXTENSIONS
a(21)-a(28) from Giovanni Resta, Jun 24 2015
a(1)-a(28) checked by Robert G. Wilson v, Jul 30 2015
a(29)-a(30) from Robert G. Wilson v, Jul 30 2015
STATUS
approved