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A319133 a(1) = a(2) = 1; for n > 2, a(n+2) = Sum_{d|n} tau(n/d)*a(d), where tau = number of divisors (A000005).

%I A319133 #9 Sep 12 2018 15:07:23
%S A319133 1,1,1,3,3,8,5,16,7,29,12,41,14,76,16,92,28,142,30,185,32,268,48,298,
%T A319133 50,466,59,500,80,683,82,817,84,1072,114,1134,134,1583,136,1649,170,
%U A319133 2176,172,2444,174,3032,239,3134,241,4174,254,4353,316,5343,318,5815,352,7121,418,7287,420,9357,422,9527,525
%N A319133 a(1) = a(2) = 1; for n > 2, a(n+2) = Sum_{d|n} tau(n/d)*a(d), where tau = number of divisors (A000005).
%H A319133 Antti Karttunen, <a href="/A319133/b319133.txt">Table of n, a(n) for n = 1..4240</a>
%H A319133 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%t A319133 a[1] = a[2] = 1; a[n_] := a[n] = Sum[DivisorSigma[0, (n - 2)/d] a[d], {d, Divisors[n - 2]}]; Table[a[n], {n, 65}]
%o A319133 (PARI) A319133(n) = if(n<=2,1,sumdiv(n-2,d,numdiv((n-2)/d)*A319133(d))); \\ (non-memoized implementation) - _Antti Karttunen_, Sep 11 2018
%o A319133 (PARI)
%o A319133 \\ Faster implementation:
%o A319133 up_to = 4240;
%o A319133 A319133list(up_to) = { my(u=vector(up_to)); u[1] = u[2] = 1; for(n=3, up_to, u[n] = sumdiv(n-2,d,numdiv((n-2)/d)*u[d])); (u); };
%o A319133 v319133 = A319133list(up_to);
%o A319133 A319133(n) = v319133[n]; \\ _Antti Karttunen_, Sep 11 2018
%Y A319133 Cf. A000005, A003238, A007439, A007557, A318583.
%K A319133 nonn
%O A319133 1,4
%A A319133 _Ilya Gutkovskiy_, Sep 11 2018