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a(n) = Sum_{k = 1..n} u_3(k), where u_3 = A034836.
1

%I #13 Apr 19 2024 03:30:14

%S 1,2,3,5,6,8,9,12,14,16,17,21,22,24,26,30,31,35,36,40,42,44,45,51,53,

%T 55,58,62,63,68,69,74,76,78,80,88,89,91,93,99,100,105,106,110,114,116,

%U 117,126,128,132,134,138,139,145,147,153,155,157,158,168,169,171,175,182,184,189,190,194,196,201,202,214,215,217

%N a(n) = Sum_{k = 1..n} u_3(k), where u_3 = A034836.

%C For background references see A330570.

%H Amiram Eldar, <a href="/A331072/b331072.txt">Table of n, a(n) for n = 1..10000</a>

%t s[1] = 1; 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]; Accumulate[Array[s, 100]] (* _Amiram Eldar_, Apr 19 2024 *)

%Y Cf. A034836.

%Y A096276 has the same initial terms, but is a different sequence.

%K nonn

%O 1,2

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