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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).
5
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 11 2018
STATUS
approved