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A348955 a(1) = 1; a(n) = Sum_{d|n, d <= sqrt(n)} a(d)^2.

%I A348955 #9 Dec 14 2021 12:10:17
%S A348955 1,1,1,2,1,2,1,2,2,2,1,3,1,2,2,6,1,3,1,6,2,2,1,7,2,2,2,6,1,4,1,6,2,2,
%T A348955 2,11,1,2,2,7,1,7,1,6,3,2,1,11,2,3,2,6,1,7,2,7,2,2,1,12,1,2,3,10,2,7,
%U A348955 1,6,2,4,1,15,1,2,3,6,2,7,1,11,6,2,1,12,2,2,2,10,1,12
%N A348955 a(1) = 1; a(n) = Sum_{d|n, d <= sqrt(n)} a(d)^2.
%H A348955 Antti Karttunen, <a href="/A348955/b348955.txt">Table of n, a(n) for n = 1..20000</a>
%F A348955 G.f.: Sum_{k>=1} a(k)^2 * x^(k^2) / (1 - x^k).
%F A348955 a(4^n) = A067868(n).
%t A348955 a[1] = 1; a[n_] := a[n] = DivisorSum[n, a[#]^2 &, # <= Sqrt[n] &]; Table[a[n], {n, 90}]
%o A348955 (PARI) A348955(n) = if(1==n,n,sumdiv(n,d,if((d*d)<=n,A348955(d)^2,0))); \\ _Antti Karttunen_, Nov 05 2021
%Y A348955 Cf. A008578 (positions of 1's), A067868, A068108, A082588, A337135, A348956.
%K A348955 nonn
%O A348955 1,4
%A A348955 _Ilya Gutkovskiy_, Nov 04 2021