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A056798
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Prime powers with even exponents >=0.
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12
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1, 4, 9, 16, 25, 49, 64, 81, 121, 169, 256, 289, 361, 529, 625, 729, 841, 961, 1024, 1369, 1681, 1849, 2209, 2401, 2809, 3481, 3721, 4096, 4489, 5041, 5329, 6241, 6561, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 14641, 15625, 16129, 16384
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OFFSET
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1,2
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COMMENTS
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Also numbers n for which the geometric mean of divisors of n is an integer. - Ctibor O. Zizka, Sep 29 2008
This is just a special case. In fact, the numbers n for which the geometric mean of divisors of n is an integer are all the squares of integers (A000290). - Daniel Lignon, Nov 29 2014
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A025473(n)^(2*A025474(n)) = A000961(n)^2;
A001222(a(n)) mod 2 = 0;
A003415(a(n)) = A192083(n); A068346(a(n)) = A192084(n). - Reinhard Zumkeller, Jun 26 2011
Sum_{n>=2} 1/a(n) = A154945. - Amiram Eldar, Sep 21 2020
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MATHEMATICA
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Take[Union[Flatten[Table[Prime[n]^k, {n, 31}, {k, 0, 14, 2}]]], 45] (* Alonso del Arte, Jul 05 2011 *)
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PROG
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(PARI) is(n)=my(e=isprimepower(n)); if(e, e%2==0, n==1) \\ Charles R Greathouse IV, Sep 18 2015
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CROSSREFS
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Cf. A000961, A025475, A154945.
Sequence in context: A069560 A075494 A063735 * A036454 A115648 A082522
Adjacent sequences: A056795 A056796 A056797 * A056799 A056800 A056801
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Aug 28 2000
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STATUS
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approved
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