

A181092


a(n) is the sum of n addends nested as follows: floor(sqrt(floor(sqrt(...(n)...)))).


2



1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80
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OFFSET

1,2


COMMENTS

a(n)=n+k(n) k has an increment of at least 1 unit when n is a perfect square.
The converse is not true:
Its complement is 4, 10, 18, 19, 29, 41, 55, 71, 89, 90, 110, 132, 156, 182, 210, 240, ....  Robert G. Wilson v, Nov 15 2012


LINKS

Carmine Suriano, Table of n, a(n) for n = 1..2010


FORMULA

a(n) = n + sqrt(n) + O(n^(1/4)).  Charles R Greathouse IV, Nov 15 2012


EXAMPLE

a(5)=6 since floor(sqrt(5))=2; floor(sqrt(2))=1; floor(sqrt(1))=1 for the remaining three additional iterations.


MATHEMATICA

f[n_] := Plus @@ Rest@ NestList[ Floor@ Sqrt@# &, n, n]; Array[f, 72] (* Robert G. Wilson v, Nov 15 2012 *)


PROG

(PARI) a(n)=my(k=n, s); while((n=sqrtint(n))>1, s+=n; k); s+k \\ Charles R Greathouse IV, Nov 15 2012


CROSSREFS

Cf. A219227.
Sequence in context: A247360 A145397 A183570 * A184526 A047256 A039252
Adjacent sequences: A181089 A181090 A181091 * A181093 A181094 A181095


KEYWORD

nonn,easy


AUTHOR

Carmine Suriano, Oct 02 2010


STATUS

approved



