A032515 Sum of the integer part of 5/2-th roots of integers less than or equal to n.

0, 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 174, 179, 184, 189, 194, 199

Offset

0,3

Links

Table of n, a(n) for n=0..61.

Formula

a(0) = 0, a(n) = a(n - 1) + floor(n^(2/5)). - Alonso del Arte, Jun 18 2017

a(n) = (5/7)*n^(7/5) + O(n). - Charles R Greathouse IV, Jun 25 2017

Example

1^(2/5) = 1.
2^(2/5) = 1.3195...
3^(2/5) = 1.5518...
4^(2/5) = 1.7411...
5^(2/5) = 1.90365...
6^(2/5) = 2.047672511...
Hence a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5, a(6) = 7.

Mathematica

Accumulate[Table[Floor[n^(2/5)], {n, 0, 59}]] (* Alonso del Arte, Jun 13 2017 *)

Prog

(PARI) a(n)=sum(k=1, n, sqrtnint(k^2, 5)) \\ Charles R Greathouse IV, Jun 25 2017

Crossrefs

Sequence in context: A004276 A033057 A092755 * A024926 A051532 A325461

Adjacent sequences: A032512 A032513 A032514 * A032516 A032517 A032518

Keyword

nonn,easy

Author

Michel Tixier (tixier(AT)dyadel.net)

Status

approved