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

Author

Michel Tixier (tixier(AT)dyadel.net)

Keywords

• nonn
• easy

Examples

			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.
		

Programs

Mathematica

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

PARI

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

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