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%I #27 May 15 2021 12:34:59
%S 1,2,2,11,47,46,983,193534,676644395
%N a(1) = 1, otherwise smallest m > 1 such that the sum of digits of m^n is k^n for some k > 1.
%C n-th root of A069647(n).
%C Probably k = 2 in all cases. - _Charles R Greathouse IV_, Feb 26 2014
%F a(n) > c^2^n for n > 1 where c = 10^(1/81) = 1.0288.... - _Charles R Greathouse IV_, Feb 26 2014
%o (Python)
%o import sympy
%o from sympy import factorint
%o def DigitSum(x):
%o return sum(int(i) for i in str(x))
%o def PowExp(p):
%o n = 2
%o while n < 10000*(10**(int(2**p/9)/p)):
%o if DigitSum(n**p) != 1:
%o count = 0
%o for i in list(factorint(DigitSum(n**p)).values()):
%o if (int(i)/p) % 1 == 0:
%o count += 1
%o if count == len(list(factorint(DigitSum(n**p)).values())):
%o return n
%o else:
%o n += 1
%o else:
%o n += 1
%o print(1)
%o x = 2
%o while x < 20:
%o print(PowExp(x))
%o x += 1
%o # _Derek Orr_, Feb 16 2014
%o (PARI)
%o a237992(maxn, maxm) = {
%o print1("1, ");
%o for(n=1, maxn,
%o for(m=2, maxm,
%o t=eval(Vec(Str(m^n)));
%o d=sum(i=1, #t, t[i]);
%o if(d>1 && ispower(d, n), print1(m, ", "); break())
%o )
%o )
%o }
%o a237992(8, 1000000) \\ _Colin Barker_, Feb 23 2014
%o (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
%o (Python)
%o from sympy import factorint
%o def A069648(n):
%o ....if (n == 1):
%o ........return 1
%o ....else:
%o ........m = 2
%o ........while True:
%o ............x = sum(int(d) for d in str(m**n))
%o ............if x > 1 and not any(map(lambda x:x%n,factorint(x).values())):
%o ................return m
%o ............m += 1 # _Chai Wah Wu_, Aug 11 2014
%Y Cf. A069647.
%K more,nonn,base
%O 1,2
%A _Amarnath Murthy_, Apr 04 2002
%E Corrected and extended by _David Wasserman_, Apr 23 2003
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