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

Author

Balarka Sen, Apr 30 2013

Keywords

• nonn
• easy
• changed

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

Crossrefs

Cf. A022819, A025224.

Programs

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

Formula

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