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A216658 Number of n-digit 8th powers.

%I A216658 #11 Sep 15 2024 19:30:27
%S A216658 2,0,1,1,1,1,2,2,4,4,6,8,11,14,18,25,34,44,60,79,105,141,187,250,334,
%T A216658 445,593,791,1054,1407,1875,2501,3336,4447,5931,7909,10547,14065,
%U A216658 18755,25010,33353,44475,59310,79090,105469,140645,187553,250105,333522,444758
%N A216658 Number of n-digit 8th powers.
%H A216658 Alois P. Heinz, <a href="/A216658/b216658.txt">Table of n, a(n) for n = 1..1000</a>
%e A216658 a(1) = 2: 0, 1.
%e A216658 a(3) = 1: 256.
%e A216658 a(4) = 1: 6561.
%e A216658 a(9) = 4: 100000000, 214358881, 429981696, 815730721.
%e A216658 a(10) = 4: 1475789056, 2562890625, 4294967296, 6975757441.
%e A216658 a(11) = 6: 11019960576, 16983563041, 25600000000, 37822859361, 54875873536, 78310985281.
%p A216658 r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k<n, 1, 0) end:
%p A216658 a:= n-> r(10^n, 8) -r(10^(n-1), 8) +`if`(n=1, 1, 0):
%p A216658 seq(a(n), n=1..60);
%t A216658 Join[{2,0},Tally[IntegerLength[Range[2,18*10^5]^8]][[;;,2]]] (* _Harvey P. Dale_, Sep 15 2024 *)
%Y A216658 Column k=8 of A216653.
%K A216658 nonn,base
%O A216658 1,1
%A A216658 _Alois P. Heinz_, Sep 12 2012