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A352788 Squares in A213544.

%I A352788 #10 Apr 08 2022 10:47:28
%S A352788 1,9,25,10510564
%N A352788 Squares in A213544.
%C A352788 Squares that are partial sums of A023896.
%e A352788 a(3) = 25 is a term because A213544(6) = 25 = 5^2.
%p A352788 s:= 1: R:= 1: count:= 1:
%p A352788 for n from 2 to 10^6 do
%p A352788 s:= s + n/2*numtheory:-phi(n);
%p A352788   if issqr(s) then
%p A352788      count:= count+1; R:= R, s;
%p A352788   fi;
%p A352788 od:
%p A352788 R;
%t A352788 f[1] = 1; f[n_] := n*EulerPhi[n]/2; seq[len_, max_] := Module[{s = {}, sum = 0, c = 0, n = 1}, While[c < len && n < max, sum += f[n]; n++; If[IntegerQ@Sqrt[sum], c++; AppendTo[s, sum]]]; s]; seq[4, 1000] (* _Amiram Eldar_, Apr 07 2022 *)
%o A352788 (Python)
%o A352788 from itertools import count, islice
%o A352788 from sympy import totient
%o A352788 def A352788_gen(): # generator of terms
%o A352788     c, m, ms = 0, 1, 1
%o A352788     for n in count(1):
%o A352788         c += 1 if n <= 2 else n*totient(n)//2
%o A352788         if c == ms:
%o A352788             yield c
%o A352788         else:
%o A352788             while c > ms:
%o A352788                 ms += 2*m+1
%o A352788                 m += 1
%o A352788 A352788_list = list(islice(A352788_gen(),4)) # _Chai Wah Wu_, Apr 08 2022
%Y A352788 Cf. A000290, A023896, A213544.
%K A352788 nonn,more
%O A352788 1,2
%A A352788 _Robert Israel_, Apr 02 2022