A174724 Sum_{k=1..n} Floor((k + 3*sqrt(k))/k).

4, 7, 9, 11, 13, 15, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset

1,1

Links

Table of n, a(n) for n=1..65.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

(k+3*sqrt(k)) / k > = 1, (k+3*sqrt(k)) / k < 2 <=> k >=10, a(n) = 4 if n=1, a(n) = 2n + 3 if 2 <= n <= 9, a(n) = n + 12 if n>=10.

Maple

for n from 1 to 100 do: s:=0: for k from 1 to n do: s:=s+floor((k+3*sqrt(k))/k) : od:print(s):od:

Mathematica

Accumulate[Table[Floor[(k+3*Sqrt[k])/k], {k, 70}]] (* Harvey P. Dale, Apr 27 2022 *)

Prog

(PARI) a(n)=if(n>8, n+12, 2*n+3-(n==1)) \\ Charles R Greathouse IV, Oct 27 2011

Crossrefs

Sequence in context: A159619 A272454 A207017 * A267873 A310943 A310944

Adjacent sequences: A174721 A174722 A174723 * A174725 A174726 A174727

Keyword

nonn,easy

Author

Michel Lagneau, Mar 28 2010

Status

approved