

A270540


Numbers that are equal to the number of their digits multiplied by the sum of the fifth powers of the digits.


0




OFFSET

1,3


COMMENTS

Terms up to 10^8.
No further terms after 10^7 since 10^k > k^2*9^5 beyond that point.  Ray Chandler, Apr 01 2016


LINKS



EXAMPLE

4100 is a term because 4100 = 4*(4^5+1^5+0^5+0^5).


MATHEMATICA

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}
Select[Range[10^7], With[{id=IntegerDigits[#]}, #==Length[id]*Plus@@(id^5)]&] (* Ray Chandler, Apr 01 2016 *)


PROG

(PARI) isok(n) = my(d=digits(n)); n == #d*sum(k=1, #d, d[k]^5); \\ Michel Marcus, Mar 25 2016


CROSSREFS



KEYWORD

nonn,base,fini,full


AUTHOR



EXTENSIONS



STATUS

approved



