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A062320 Nonsquarefree numbers squared. A013929(n)^2.

%I A062320 #30 Sep 18 2024 11:21:50
%S A062320 16,64,81,144,256,324,400,576,625,729,784,1024,1296,1600,1936,2025,
%T A062320 2304,2401,2500,2704,2916,3136,3600,3969,4096,4624,5184,5625,5776,
%U A062320 6400,6561,7056,7744,8100,8464,9216,9604,9801,10000,10816,11664,12544,13456
%N A062320 Nonsquarefree numbers squared. A013929(n)^2.
%C A062320 A008966(A037213(a(n))) = 0. - _Reinhard Zumkeller_, Sep 03 2015
%H A062320 Harry J. Smith, <a href="/A062320/b062320.txt">Table of n, a(n) for n = 1..1000</a>
%F A062320 Sum_{n>=1} 1/a(n) = Pi^2/6 - 15/Pi^2. - _Amiram Eldar_, Jul 16 2020
%o A062320 (PARI) for(n=1,55, if(issquarefree(n), n+1,print(n^2)))
%o A062320 (PARI) n=-1; for (m=1, 10^9, if (!issquarefree(m), write("b062320.txt", n++, " ", m^2); if (n==1000, break))) \\ _Harry J. Smith_, Aug 04 2009
%o A062320 (PARI) is(n)=issquare(n,&n) && !issquarefree(n) \\ _Charles R Greathouse IV_, Sep 18 2015
%o A062320 (Haskell)
%o A062320 a062320 = (^ 2) . a013929 -- _Reinhard Zumkeller_, Sep 03 2015
%o A062320 (Python)
%o A062320 from math import isqrt
%o A062320 from sympy import mobius
%o A062320 def A062320(n):
%o A062320     def f(x): return n+1+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
%o A062320     def bisection(f,kmin=0,kmax=1):
%o A062320         while f(kmax) > kmax: kmax <<= 1
%o A062320         while kmax-kmin > 1:
%o A062320             kmid = kmax+kmin>>1
%o A062320             if f(kmid) <= kmid:
%o A062320                 kmax = kmid
%o A062320             else:
%o A062320                 kmin = kmid
%o A062320         return kmax
%o A062320     return bisection(f)**2 # _Chai Wah Wu_, Aug 31 2024
%Y A062320 Cf. A013929, A008966, A037213, A320965.
%Y A062320 Squares in A046099.
%K A062320 easy,nonn
%O A062320 1,1
%A A062320 _Jason Earls_, Jul 05 2001
%E A062320 More terms from Larry Reeves (larryr(AT)acm.org), Jul 11 2001
%E A062320 Offset corrected by _Andrew Howroyd_, Sep 18 2024