A066508 a(n) = floor(Sum_{i=1..n} (1/i)^(1/i)).

1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 57, 58, 59, 60, 61, 62, 63, 64

Offset

1,3

Comments

a(n) = floor(Sum_{i=1..n} (1/i)^(1/i)) = floor(Sum_{i=1..n} i^(-1/i)).

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

a(n) = n - log(n)^2/2 + O(1) as n -> infinity. - Robert Israel, Jan 05 2016

Example

For a(5), 1^1 + (1/2)^(1/2) + (1/3)^(1/3) + (1/4)^(1/4) + (1/5)^(1/5) ~= 3.8323545. Therefore a(5) = 3.

Maple

A066508:=n->floor(add((1/i)^(1/i), i=1..n)): seq(A066508(n), n=1..100); # Wesley Ivan Hurt, Jan 03 2016

Mathematica

Table[ Floor[ Sum[ (1/i)^(1/i), {i, n} ]], {n, 75} ]
Floor[Accumulate[With[{nn=75}, (1/Range[nn])^(1/Range[nn])]]] (* Harvey P. Dale, Oct 05 2022 *)

Prog

(PARI) { s=0; for (n=1, 1000, s+=(1/n)^(1/n); write("b066508.txt", n, " ", floor(s)) ) } \\ Harry J. Smith, Feb 19 2010
(PARI) a(n) = floor(sum(i=1, n, (1/i)^(1/i))); \\ Michel Marcus, Jan 04 2016

Crossrefs

Cf. A001008, A002805, A067054.

Sequence in context: A214449 A118168 A083920 * A319413 A307727 A309081

Adjacent sequences: A066505 A066506 A066507 * A066509 A066510 A066511

Keyword

nonn,easy

Author

Robert G. Wilson v, Jan 04 2002

Extensions

Example corrected by Harry J. Smith, Feb 19 2010

Status

approved