A117732 - OEIS

%I #19 Aug 20 2021 04:21:59

%S 1,2,3,4,5,6,7,8,9,24,27,48,81,192,243,288,375,392,486,512,576,648,

%T 729,864,972,1296,1458,1728,1944,2187,2401,2592,2916,3456,4374,4608,

%U 4802,4913,5184,5832,6561,6912,10368,11664,13824,15552,17576,19683,20736,23328

%N Numbers k that divide s(k)^w(k), where s(k) is the sum of the digits of k and w(k) is the digital root of k.

%e 392 is in the sequence because (1) s(392) = 3 + 9 + 2 = 14 and w(392) = 1 + 4 = 5, and (2) 14^5 = 537824 is divisible by 392.

%t Select[Range[10^5],Divisible[Total@IntegerDigits@#^FixedPoint[Total@IntegerDigits@#&,#],#]&] (* _Giorgos Kalogeropoulos_, Aug 20 2021 *)

%o (PARI) a010888(n) = (n-1)%9+1;

%o isok(n) = !(sumdigits(n)^a010888(n) % n); \\ _Michel Marcus_, Feb 27 2014

%Y Cf. A007953, A010888.

%K base,nonn

%O 1,2

%A Luc Stevens (lms022(AT)yahoo.com), Apr 14 2006

%E Corrected by _Michel Marcus_, Feb 27 2014