A352077 a(n) = floor( Sum_{k=1..n} k^(1/3) ).

0, 1, 2, 3, 5, 6, 8, 10, 12, 14, 16, 19, 21, 23, 26, 28, 31, 33, 36, 39, 41, 44, 47, 50, 53, 56, 58, 61, 65, 68, 71, 74, 77, 80, 83, 87, 90, 93, 97, 100, 104, 107, 110, 114, 117, 121, 125, 128, 132, 136, 139, 143, 147, 150, 154, 158, 162, 166, 170, 173, 177, 181, 185, 189, 193, 197

Offset

0,3

Links

Table of n, a(n) for n=0..65.

Snehal Shekatkar, On the sum of the r'th roots of first n natural numbers, arXiv:1204.0877 [math.NT], 2012-2013.

Example

a(6) = 8 because 1^(1/3) + 2^(1/3) + 3^(1/3) + 4^(1/3) + 5^(1/3) + 6^(1/3) = 8.81667... .

Mathematica

a[n_] := Floor[ HarmonicNumber[n, -1/3]]; Array[ a, 66, 0]

Prog

(PARI) a(n) = floor(sum(k=0, n, k^(1/3))); \\ Michel Marcus, Mar 02 2022

Crossrefs

Cf. A031876, A025224.

Sequence in context: A366968 A080276 A120836 * A213857 A011864 A045919

Adjacent sequences: A352074 A352075 A352076 * A352078 A352079 A352080

Keyword

easy,nonn

Author

Robert G. Wilson v, Mar 02 2022

Status

approved