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A161203 n-th square plus n-th squarefree number.

%I A161203 #28 Aug 13 2024 02:25:58
%S A161203 2,6,12,21,31,43,59,75,94,114,136,161,188,217,247,279,315,353,391,431,
%T A161203 474,518,564,613,663,715,770,826,884,946,1008,1075,1142,1211,1282,
%U A161203 1354,1428,1505,1583
%N A161203 n-th square plus n-th squarefree number.
%F A161203 a(n) = n^2 + A005117(n) = A000290(n) + A005117(n).
%e A161203 a(1) = 1^2 + 1.
%e A161203 a(2) = 2^2 + 2.
%e A161203 a(3) = 3^2 + 3.
%e A161203 a(4) = 4^2 + 5.
%t A161203 Module[{nn=40,sqs,sfree},sqs=Range[nn]^2;sfree=Take[Select[Range[3nn], SquareFreeQ],nn];Total/@Thread[{sqs,sfree}]] (* _Harvey P. Dale_, May 06 2012 *)
%o A161203 (Python)
%o A161203 from math import isqrt
%o A161203 from sympy import mobius
%o A161203 def A161203(n):
%o A161203     def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
%o A161203     m, k = n, f(n)
%o A161203     while m != k:
%o A161203         m, k = k, f(k)
%o A161203     return m+n**2 # _Chai Wah Wu_, Aug 12 2024
%Y A161203 Cf. A000290, A005117.
%K A161203 nonn,easy
%O A161203 1,1
%A A161203 _Jonathan Vos Post_, Jan 20 2011
%E A161203 Corrected (75 inserted) by _Harvey P. Dale_, May 06 2012