A307982 - OEIS

%I #17 May 11 2019 18:32:34

%S 1,1,1,1,1,3,3,6,3,11,5,15,8,19,7,36,10,31,15,60,12,56,17,97,24,72,19,

%T 170,29,94,32,229,31,156,34,334,47,182,46,471,49,218,68,658,51,314,70,

%U 797,84,354,72,1173,93,437,98,1353,95,576,114,1792,131,640,116,2243,133

%N G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 * (1 + Sum_{i>=1} Sum_{j>=1} A(x^(i*j))).

%C Shifts 4 places left when inverse Moebius transform applied twice.

%F a(1) = ... = a(4) = 1; a(n+4) = Sum_{d|n} tau(n/d)*a(d), where tau = number of divisors (A000005).

%t a[n_] := a[n] = Sum[DivisorSigma[0, (n - 4)/d] a[d], {d, Divisors[n - 4]}]; a[1] = a[2] = a[3] = a[4] = 1; Table[a[n], {n, 1, 65}]

%Y Cf. A000005, A007557, A307967, A307994, A308083, A319133.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, May 11 2019