A331076 - OEIS

%I #12 Apr 19 2024 03:27:29

%S 0,1,1,2,3,4,5,8,8,11,11,16,16,19,18,29,24,31,28,39,34,43,36,60,44,57,

%T 49,71,55,75,61,93,73,90,71,118,83,107,93,135,95,135,102,152,118,147,

%U 112,202,126,169,145,203,139,211,147,233,177,215,160,286

%N a(n) = Sum_{k = 1..ceiling(n/2)} [u_3(k)*u_3(n+1-k)], where u_3 = A034836.

%C For background references see A330570.

%H Amiram Eldar, <a href="/A331076/b331076.txt">Table of n, a(n) for n = 0..10000</a>

%t s[1] = 1; s[n_] := s[n] = Module[{e = FactorInteger[n][[;; , 2]]}, If[IntegerQ[Surd[n, 3]], 1/3, 0] + (Times @@ ((e + 1)*(e + 2)/2))/6 + (Times @@ (Floor[e/2] + 1))/2]; a[n_] := Sum[s[k] * s[n+1-k], {k, 1, Ceiling[n/2]}]; Array[a, 100, 0] (* _Amiram Eldar_, Apr 19 2024 *)

%Y Cf. A034836.

%Y See A331075 for another version.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Jan 10 2020

%E Offset and name corrected by _Amiram Eldar_, Apr 19 2024