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A117926
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a(n) = n^floor(sqrt(n)).
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1
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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
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1,2
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COMMENTS
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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].
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = n^floor(sqrt(n)) = n^floor(n^(1/2)) = n^A000196(n).
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MAPLE
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seq(n^floor(sqrt(n)), n=1..100); # Robert Israel, Jun 22 2015
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MATHEMATICA
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Table[n^Floor[Sqrt[n]], {n, 50}] (* Vincenzo Librandi, Jun 22 2015 *)
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PROG
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(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
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CROSSREFS
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Cf. A000196.
Sequence in context: A261840 A100643 A067037 * A185251 A092503 A147662
Adjacent sequences: A117923 A117924 A117925 * A117927 A117928 A117929
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, May 03 2006
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STATUS
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approved
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