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%I #20 Jul 02 2022 09:28:51
%S 4,9,25,36,49,100,121,144,169,196,225,289,324,361,400,441,484,529,576,
%T 676,784,841,900,961,1089,1156,1225,1369,1444,1521,1600,1681,1764,
%U 1849,1936,2025,2116,2209,2304,2500,2601,2704,2809,2916,3025,3136,3249,3364
%N a(n) = A007916(n)^2.
%H Reinhard Zumkeller, <a href="/A153158/b153158.txt">Table of n, a(n) for n = 1..1000</a>
%F GCD(exponents in prime factorization of a(n)) = 2, cf. A124010. - _Reinhard Zumkeller_, Apr 13 2012
%F 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
%e 2^2 = 4, 3^2 = 9, 4^2 = 16 = 2^4 is not in the sequence, 5^2 = 25, 6^2 = 36, ...
%t Select[Range[2,100],GCD@@Last/@FactorInteger@#==1&]^2
%o (Haskell)
%o a153158 n = a153158_list !! (n-1)
%o a153158_list = filter ((== 2) . foldl1 gcd . a124010_row) [2..]
%o -- _Reinhard Zumkeller_, Apr 13 2012
%Y Cf. A007916, A153147, A153157, A153159, A153160, A062503.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Dec 19 2008
%E Edited by _Ray Chandler_, Dec 22 2008
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