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A082588 a(1) = 1, a(n) = Sum_{d | n and d < n} a(d)^2 for n > 1.

%I A082588 #21 Oct 28 2018 08:36:51
%S A082588 1,1,1,2,1,3,1,6,2,3,1,16,1,3,3,42,1,16,1,16,3,3,1,308,2,3,6,16,1,31,
%T A082588 1,1806,3,3,3,532,1,3,3,308,1,31,1,16,16,3,1,96936,2,16,3,16,1,308,3,
%U A082588 308,3,3,1,1508,1,3,16,3263442,3,31,1,16,3,31,1,378456
%N A082588 a(1) = 1, a(n) = Sum_{d | n and d < n} a(d)^2 for n > 1.
%C A082588 The positions of records are A029744. - _Andrey Zabolotskiy_, Jan 30 2017
%H A082588 Andrey Zabolotskiy, <a href="/A082588/b082588.txt">Table of n, a(n) for n = 1..10000</a>
%F A082588 a(p^(n+1)) = A007018(n) if p is a prime. - _Michael Somos_, May 19 2018
%e A082588 a(12) = a(1)^2 + a(2)^2 + a(3)^2 + a(4)^2 + a(6)^2 = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 = 1 + 1 + 1 + 4 + 9 = 16.
%t A082588 a[ n_] := If[ n < 2, Boole[n == 1], Sum[ a[d]^2, {d, Drop[Divisors @ n, -1]}]]; (* _Michael Somos_, May 19 2018 *)
%o A082588 (Python)
%o A082588 a = [1]
%o A082588 for n in range(2, 10001):
%o A082588    a.append(sum(a[d-1]**2 for d in range(1, n) if n%d == 0))
%o A082588 print(a)
%o A082588 # _Andrey Zabolotskiy_, Jan 30 2017
%o A082588 (PARI) a(n) = if (n==1, 1, sumdiv(n, d, if (d<n, a(d)^2))); \\ _Michel Marcus_, Jan 30 2017
%Y A082588 Cf. A002033, A007018.
%K A082588 nonn
%O A082588 1,4
%A A082588 _Reinhard Zumkeller_, May 13 2003
%E A082588 Typo in data corrected by _Andrey Zabolotskiy_, Jan 30 2017