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a(1)=1; for n > 1, a(n) = n - a(n-floor(sqrt(n))).
2

%I #16 Dec 27 2020 16:50:31

%S 1,1,2,3,3,3,4,5,6,6,6,6,7,8,9,10,10,10,10,10,11,12,13,14,15,15,15,15,

%T 15,15,16,17,18,19,20,21,21,21,21,21,21,21,22,23,24,25,26,27,28,28,28,

%U 28,28,28,28,28,29,30,31,32,33,34,35,36,36,36,36,36,36,36,36,36,37,38

%N a(1)=1; for n > 1, a(n) = n - a(n-floor(sqrt(n))).

%F a(n) = (1/2)*(n + A053615(n)).

%o (PARI) a(n)=if(n<2,1,n-a(n-sqrtint(n)))

%Y Cf. A028391, A053615.

%K nonn

%O 1,3

%A _Benoit Cloitre_, Dec 22 2002

%E Corrected by _Franklin T. Adams-Watters_, Oct 25 2006