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).

1, 1, 1, 3, 3, 8, 5, 16, 7, 29, 12, 41, 14, 76, 16, 92, 28, 142, 30, 185, 32, 268, 48, 298, 50, 466, 59, 500, 80, 683, 82, 817, 84, 1072, 114, 1134, 134, 1583, 136, 1649, 170, 2176, 172, 2444, 174, 3032, 239, 3134, 241, 4174, 254, 4353, 316, 5343, 318, 5815, 352, 7121, 418, 7287, 420, 9357, 422, 9527, 525

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..4240

N. J. A. Sloane, Transforms

Mathematica

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}]

Prog

(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
(PARI)
\\ Faster implementation:
up_to = 4240;
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); };
v319133 = A319133list(up_to);
A319133(n) = v319133[n]; \\ Antti Karttunen, Sep 11 2018

Crossrefs

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

Sequence in context: A279727 A267092 A272212 * A266560 A021751 A302675

Adjacent sequences: A319130 A319131 A319132 * A319134 A319135 A319136

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 11 2018

Status

approved