A319133 - OEIS

%I #9 Sep 12 2018 15:07:23

%S 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 50,466,59,500,80,683,82,817,84,1072,114,1134,134,1583,136,1649,170,

%U 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 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 Antti Karttunen, <a href="/A319133/b319133.txt">Table of n, a(n) for n = 1..4240</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%t 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 (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 (PARI)

%o \\ Faster implementation:

%o up_to = 4240;

%o 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 v319133 = A319133list(up_to);

%o A319133(n) = v319133[n]; \\ _Antti Karttunen_, Sep 11 2018

%Y Cf. A000005, A003238, A007439, A007557, A318583.

%K nonn

%O 1,4

%A _Ilya Gutkovskiy_, Sep 11 2018