A231405 Least integer j such that Sum_{i=1..j} 1/i^(1/3) >= n.

1, 1, 3, 4, 6, 8, 10, 12, 15, 17, 20, 23, 25, 28, 32, 35, 38, 41, 45, 49, 52, 56, 60, 64, 68, 72, 76, 81, 85, 89, 94, 98, 103, 108, 113, 117, 122, 127, 132, 138, 143, 148, 153, 159, 164, 170, 175, 181, 187, 192, 198, 204, 210, 216, 222, 228, 234, 240, 247, 253

Offset: 0

Author

Carmine Suriano, Nov 08 2013

Keywords

• nonn

Examples

			a(7)=12 since Sum_{i=1..12} 1/i^(1/3) = 7.106248... and Sum_{i=1..11} 1/i^(1/3) = 6.669458... .
		

Links

• Sela Fried, On the partial sums of the Zeta function Sum_{n>=1} 1/n^s for 0 < s < 1, 2024.

Crossrefs

Cf. A004080, A054040, A054041 (condition >n).

Cf. A067086.

Programs

JavaScript

s=0;n=1;
for (i=1;i<30;i++) {
s+=1/Math.pow(i,1/3);
if (s>=n) {n++;document.write(Math.floor(i)+", ");}
}

Mathematica

s = 0; i = 0; Table[i++; While[s = s + 1/(i^(1/3)); s < n, i++]; i, {n, 100}] (* T. D. Noe, Nov 09 2013 *)
Module[{nn=300,c},c=Accumulate[1/Surd[Range[nn],3]];Table[Position[ c,?(#>=n&),1,1],{n,0,60}]]//Flatten (* _Harvey P. Dale, Aug 14 2021 *)

Extensions

a(0) added by Jon Perry, Nov 10 2013