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