OFFSET
1,2
COMMENTS
n-th root of A069647(n).
Probably k = 2 in all cases. - Charles R Greathouse IV, Feb 26 2014
FORMULA
a(n) > c^2^n for n > 1 where c = 10^(1/81) = 1.0288.... - Charles R Greathouse IV, Feb 26 2014
PROG
(Python)
import sympy
from sympy import factorint
def DigitSum(x):
return sum(int(i) for i in str(x))
def PowExp(p):
n = 2
while n < 10000*(10**(int(2**p/9)/p)):
if DigitSum(n**p) != 1:
count = 0
for i in list(factorint(DigitSum(n**p)).values()):
if (int(i)/p) % 1 == 0:
count += 1
if count == len(list(factorint(DigitSum(n**p)).values())):
return n
else:
n += 1
else:
n += 1
print(1)
x = 2
while x < 20:
print(PowExp(x))
x += 1
# Derek Orr, Feb 16 2014
(PARI)
a237992(maxn, maxm) = {
print1("1, ");
for(n=1, maxn,
for(m=2, maxm,
t=eval(Vec(Str(m^n)));
d=sum(i=1, #t, t[i]);
if(d>1 && ispower(d, n), print1(m, ", "); break())
)
)
}
a237992(8, 1000000) \\ Colin Barker, Feb 23 2014
(PARI) a(n)=if(n==1, return(1)); my(t=2^n, t3=3^n, k, s); while((s=sumdigits(k++^n))<t || (s<t3 && s!=t) || (s>=t3 && ispower(s, n)), ); k \\ Charles R Greathouse IV, Feb 26 2014
(Python)
from sympy import factorint
def A069648(n):
....if (n == 1):
........return 1
....else:
........m = 2
........while True:
............x = sum(int(d) for d in str(m**n))
............if x > 1 and not any(map(lambda x:x%n, factorint(x).values())):
................return m
............m += 1 # Chai Wah Wu, Aug 11 2014
CROSSREFS
KEYWORD
more,nonn,base
AUTHOR
Amarnath Murthy, Apr 04 2002
EXTENSIONS
Corrected and extended by David Wasserman, Apr 23 2003
STATUS
approved