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%I #32 Apr 06 2016 02:01:25
%S 0,1,1232,4100,268542
%N Numbers that are equal to the number of their digits multiplied by the sum of the fifth powers of the digits.
%C Terms up to 10^8.
%C No further terms after 10^7 since 10^k > k^2*9^5 beyond that point. - _Ray Chandler_, Apr 01 2016
%e 4100 is a term because 4100 = 4*(4^5+1^5+0^5+0^5).
%t Position[ Table[ IntegerLength[ k] Sum[( Floor[k/10^n] - 10 Floor[k/10^(n + 1)])^5, {n, 0, IntegerLength@ k}] - k, {k, 1, 10^6}], 0] // Flatten = {1, 1232, 4100, 268542}
%t Select[Range[10^7],With[{id=IntegerDigits[#]},#==Length[id]*Plus@@(id^5)]&] (* _Ray Chandler_, Apr 01 2016 *)
%o (PARI) isok(n) = my(d=digits(n)); n == #d*sum(k=1, #d, d[k]^5); \\ _Michel Marcus_, Mar 25 2016
%Y Cf. A055014.
%K nonn,base,fini,full
%O 1,3
%A _José de Jesús Camacho Medina_, Mar 18 2016
%E a(5) from _Michel Marcus_, Mar 25 2016
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