A348955 - OEIS

%I #9 Dec 14 2021 12:10:17

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

%H Antti Karttunen, <a href="/A348955/b348955.txt">Table of n, a(n) for n = 1..20000</a>

%F G.f.: Sum_{k>=1} a(k)^2 * x^(k^2) / (1 - x^k).

%F a(4^n) = A067868(n).

%t a[1] = 1; a[n_] := a[n] = DivisorSum[n, a[#]^2 &, # <= Sqrt[n] &]; Table[a[n], {n, 90}]

%o (PARI) A348955(n) = if(1==n,n,sumdiv(n,d,if((d*d)<=n,A348955(d)^2,0))); \\ _Antti Karttunen_, Nov 05 2021

%Y Cf. A008578 (positions of 1's), A067868, A068108, A082588, A337135, A348956.

%K nonn

%O 1,4

%A _Ilya Gutkovskiy_, Nov 04 2021