A335283 - OEIS

%I #11 Dec 10 2021 11:38:29

%S 1,1,2,1,2,2,2,1,4,2,2,2,2,2,6,1,2,4,2,2,6,2,2,2,4,2,8,2,2,6,2,1,6,2,

%T 6,4,2,2,6,2,2,6,2,2,16,2,2,2,4,4,6,2,2,8,6,2,6,2,2,6,2,2,16,1,6,6,2,

%U 2,6,6,2,4,2,2,16,2,6,6,2,2,16,2,2,6,6,2,6,2,2,16,6,2,6,2,6,2,2,4,16,4,2,6,2,2,26

%N a(n) = 1 + Sum_{d|n, n/d odd, d < n} a(d).

%H Antti Karttunen, <a href="/A335283/b335283.txt">Table of n, a(n) for n = 1..20000</a>

%F G.f. A(x) satisfies: A(x) = x / (1 - x) + Sum_{k>=2} A(x^(2*k-1)).

%F G.f.: x / (1 - x) + Sum_{n>=1} a(n) * x^(3*n) / (1 - x^(2*n)).

%F a(1) = 1; a(2*n) = a(n), a(2*n+1) = 2 * A074206(2*n+1).

%t a[n_] := 1 + Sum[If[d < n && OddQ[n/d], a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 85}]

%t terms = 85; A[_] = 0; Do[A[x_] = x/(1 - x) + Sum[A[x^(2 k - 1)], {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest

%o (PARI)

%o up_to = 20000;

%o A335283lista(up_to) = {my(v = vector(up_to)); for(n=1, up_to, v[n] = 1 + sumdiv(n, d, if(d<n&&((n/d)%2), v[d], 0))); (v); };

%o v335283 = A335283lista(up_to);

%o A335283(n) = v335283[n]; \\ _Antti Karttunen_, Dec 09 2021

%Y Cf. A000079 (positions of 1's), A038550 (positions of 2's), A067824, A074206, A209229, A307779, A335062.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, May 30 2020

%E More terms from _Antti Karttunen_, Dec 09 2021