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A069648 a(1) = 1, otherwise smallest m > 1 such that the sum of digits of m^n is k^n for some k > 1. 4
1, 2, 2, 11, 47, 46, 983, 193534, 676644395 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

n-th root of A069647(n).

Probably k = 2 in all cases. - Charles R Greathouse IV, Feb 26 2014

LINKS

Table of n, a(n) for n=1..9.

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

Cf. A069647.

Sequence in context: A208967 A192824 A184237 * A275869 A175976 A095215

Adjacent sequences:  A069645 A069646 A069647 * A069649 A069650 A069651

KEYWORD

more,nonn,base

AUTHOR

Amarnath Murthy, Apr 04 2002

EXTENSIONS

Corrected and extended by David Wasserman, Apr 23 2003

STATUS

approved

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Last modified October 25 20:18 EDT 2021. Contains 348255 sequences. (Running on oeis4.)