cp's OEIS Frontend

A257786 Numbers n such that the square root of the sum of the digits times the sum of the digits of n in some power equal n.

%I A257786 #17 May 22 2025 10:21:42
%S A257786 0,1,27,376,13131,234595324075,54377519037479592374299,
%T A257786 8326623359858152426050700,1513868951125582592290131113769528
%N A257786 Numbers n such that the square root of the sum of the digits times the sum of the digits of n in some power equal n.
%C A257786 It appears that this sequence is finite.
%e A257786 376 = sqrt(3+7+6)*(3^2+7^2+6^2).
%e A257786 13131 = sqrt(1+3+1+3+1)*(1^7+3^7+1^7+3^7+1^7).
%o A257786 (Python)
%o A257786 def moda(n,a):
%o A257786     kk = 0
%o A257786     while n > 0:
%o A257786         kk= kk+(n%10)**a
%o A257786         n =int(n//10)
%o A257786     return kk
%o A257786 def sod(n):
%o A257786     kk = 0
%o A257786     while n > 0:
%o A257786         k= kk+(n%10)
%o A257786         n =int(n//10)
%o A257786     return kk
%o A257786 for a in range (1, 10):
%o A257786     for c in range (1, 10**8):
%o A257786         if c**2==sod(c)*moda(c,a)**2:
%o A257786             print (a,c, sod(c),moda(c,a))
%Y A257786 Cf. A028839, A061209, A115518, A130680.
%K A257786 base,nonn,more
%O A257786 1,3
%A A257786 _Pieter Post_, May 08 2015
%E A257786 a(6) from _Giovanni Resta_, May 09 2015
%E A257786 a(7)-a(9) from _Chai Wah Wu_, Nov 29 2015