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%I #13 Aug 20 2013 00:02:24
%S 1,2,3,5,6,7,8,9,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,30,
%T 31,32,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,50,51,52,53,54,
%U 56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,72,73,74,75,76,77,78,79,80
%N a(n) is the sum of n addends nested as follows: floor(sqrt(floor(sqrt(...(n)...)))).
%C a(n)=n+k(n) k has an increment of at least 1 unit when n is a perfect square.
%C The converse is not true:
%C Its complement is 4, 10, 18, 19, 29, 41, 55, 71, 89, 90, 110, 132, 156, 182, 210, 240, .... - _Robert G. Wilson v_, Nov 15 2012
%H Carmine Suriano, <a href="/A181092/b181092.txt">Table of n, a(n) for n = 1..2010</a>
%F a(n) = n + sqrt(n) + O(n^(1/4)). - _Charles R Greathouse IV_, Nov 15 2012
%e a(5)=6 since floor(sqrt(5))=2; floor(sqrt(2))=1; floor(sqrt(1))=1 for the remaining three additional iterations.
%t f[n_] := Plus @@ Rest@ NestList[ Floor@ Sqrt@# &, n, n]; Array[f, 72] (* _Robert G. Wilson v_, Nov 15 2012 *)
%o (PARI) a(n)=my(k=n,s);while((n=sqrtint(n))>1,s+=n;k--);s+k \\ _Charles R Greathouse IV_, Nov 15 2012
%Y Cf. A219227.
%K nonn,easy
%O 1,2
%A _Carmine Suriano_, Oct 02 2010
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