

A174059


a(n) = ceiling(Sum_{k=1..n} sqrt(k)).


1



0, 1, 3, 5, 7, 9, 11, 14, 17, 20, 23, 26, 30, 33, 37, 41, 45, 49, 53, 58, 62, 67, 71, 76, 81, 86, 91, 96, 102, 107, 113, 118, 124, 130, 135, 141, 147, 153, 160, 166, 172, 179, 185, 192, 198, 205, 212, 219, 225, 232, 240, 247, 254, 261, 269, 276, 283, 291, 299, 306
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OFFSET

0,3


LINKS

Robert Israel, Table of n, a(n) for n = 0..1000


FORMULA

a(n) = 2/3*n^(3/2) + 1/2*n^(1/2) + O(1). It appears that the absolute value of the difference is always less than 1.  Robert Israel, May 06 2019


MAPLE

map(ceil, ListTools:PartialSums([seq((sqrt(k)), k=0..100)])); # Robert Israel, May 06 2019


MATHEMATICA

s=0; lst={}; Do[s+=Sqrt[n]; AppendTo[lst, Ceiling[s]], {n, 0, 6!}]; lst
Ceiling[Accumulate[Sqrt[Range[0, 60]]]] (* Harvey P. Dale, Aug 29 2016 *)


CROSSREFS

Cf. A025224, A174058
Sequence in context: A175269 A318919 A279539 * A321676 A268292 A240992
Adjacent sequences: A174056 A174057 A174058 * A174060 A174061 A174062


KEYWORD

nonn


AUTHOR

Vladimir Joseph Stephan Orlovsky, Mar 06 2010


EXTENSIONS

Offset corrected by Robert Israel, May 06 2019


STATUS

approved



