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A153158 a(n) = A007916(n)^2.

%I A153158 #34 Nov 26 2024 17:21:21
%S A153158 4,9,25,36,49,100,121,144,169,196,225,289,324,361,400,441,484,529,576,
%T A153158 676,784,841,900,961,1089,1156,1225,1369,1444,1521,1600,1681,1764,
%U A153158 1849,1936,2025,2116,2209,2304,2500,2601,2704,2809,2916,3025,3136,3249,3364,3481
%N A153158 a(n) = A007916(n)^2.
%C A153158 A378168(n) is the number of terms <= 10^n. - _Chai Wah Wu_, Nov 21 2024
%H A153158 Reinhard Zumkeller, <a href="/A153158/b153158.txt">Table of n, a(n) for n = 1..1000</a>
%F A153158 GCD(exponents in prime factorization of a(n)) = 2, cf. A124010. - _Reinhard Zumkeller_, Apr 13 2012
%F A153158 Sum_{n>=1} 1/a(n) = zeta(2) - 1 - Sum_{k>=2} mu(k)*(1 - zeta(2*k)) = 0.5444587396... - _Amiram Eldar_, Jul 02 2022
%F A153158 Intersection of A000290 and A378287. Squares that are not of the form m^k for some k>=3. - _Chai Wah Wu_, Nov 21 2024
%e A153158 2^2 = 4, 3^2 = 9, 4^2 = 16 = 2^4 is not in the sequence, 5^2 = 25, 6^2 = 36, ...
%p A153158 q:= n-> is(igcd(seq(i[2], i=ifactors(n)[2]))=2):
%p A153158 select(q, [i^2$i=2..60])[];  # _Alois P. Heinz_, Nov 26 2024
%t A153158 Select[Range[2,100],GCD@@Last/@FactorInteger@#==1&]^2
%o A153158 (Haskell)
%o A153158 a153158 n = a153158_list !! (n-1)
%o A153158 a153158_list = filter ((== 2) . foldl1 gcd . a124010_row) [2..]
%o A153158 -- _Reinhard Zumkeller_, Apr 13 2012
%o A153158 (Python)
%o A153158 from sympy import mobius, integer_nthroot
%o A153158 def A153158(n):
%o A153158     def f(x): return int(n+1-sum(mobius(k)*(integer_nthroot(x,k)[0]-1) for k in range(2,x.bit_length())))
%o A153158     m, k = n, f(n)
%o A153158     while m != k:
%o A153158         m, k = k, f(k)
%o A153158     return m**2 # _Chai Wah Wu_, Aug 13 2024
%Y A153158 Cf. A007916, A153147, A153157, A153159, A153160, A062503, A076467, A378168, A378287.
%K A153158 nonn
%O A153158 1,1
%A A153158 _Vladimir Joseph Stephan Orlovsky_, Dec 19 2008
%E A153158 Edited by _Ray Chandler_, Dec 22 2008