A225154 Floor(sum_{i=1..n} (sum_{j=1..i} sqrt(1/j))).

1, 2, 4, 7, 11, 14, 18, 23, 27, 32, 38, 43, 49, 55, 62, 68, 75, 82, 90, 97, 105, 113, 121, 130, 138, 147, 156, 166, 175, 185, 194, 204, 214, 225, 235, 246, 257, 267, 279, 290, 301, 313, 325, 336, 349, 361, 373, 385, 398

Offset

1,2

Comments

The fact that a(n)/n diverges (it is greater than sqrt(n)) implies sum_{k>=1} 1/sqrt(k) is not Cesaro summable.

Links

Balarka Sen, Table of n, a(n) for n = 1..500

Formula

a(n) ~ 2*sum_{k=1..n} sqrt(k) ~ (4/3) n^(3/2).

Prog

(PARI) for(n=1, 100, print1(floor(sum(i=1, n, sum(j=1, i, 1/sqrt(j))))", "))
(PARI) a(n)=sum(j=1, n, (n+1-j)/sqrt(j))\1 \\ Charles R Greathouse IV, May 02 2013

Crossrefs

Cf. A022819, A025224.

Sequence in context: A192638 A211372 A054850 * A167805 A027427 A306070

Adjacent sequences: A225151 A225152 A225153 * A225155 A225156 A225157

Keyword

nonn,easy

Author

Balarka Sen, Apr 30 2013

Status

approved