

A117926


a(n) = n^floor(sqrt(n)).


1



1, 2, 3, 16, 25, 36, 49, 64, 729, 1000, 1331, 1728, 2197, 2744, 3375, 65536, 83521, 104976, 130321, 160000, 194481, 234256, 279841, 331776, 9765625, 11881376, 14348907, 17210368, 20511149, 24300000, 28629151, 33554432, 39135393
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OFFSET

1,2


COMMENTS

a(n) = n^(the integer part of the geometric mean of the divisors of n).
a(n) = n^[Card(k, 0<k<=n such that k is relatively prime to core(k)) where core(x) is the squarefree part of x].
a(n) = n^[Number of numbers k <=n with an odd number of divisors].


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = n^floor(sqrt(n)) = n^floor(n^(1/2)) = n^A000196(n).


MAPLE

seq(n^floor(sqrt(n)), n=1..100); # Robert Israel, Jun 22 2015


MATHEMATICA

Table[n^Floor[Sqrt[n]], {n, 50}] (* Vincenzo Librandi, Jun 22 2015 *)


PROG

(MAGMA) [ n^ Floor(n^(1/2)) : n in [1..40]]; // Zaki Khandaker, Jun 21 2015
(PARI) vector(50, n, n^sqrtint(n)) \\ Michel Marcus, Jun 21 2015


CROSSREFS

Cf. A000196.
Sequence in context: A261840 A100643 A067037 * A185251 A092503 A147662
Adjacent sequences: A117923 A117924 A117925 * A117927 A117928 A117929


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, May 03 2006


STATUS

approved



