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A117897
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Number of labeled trees on prime numbers of nodes through n-th prime.
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1, 4, 129, 16936, 2357964627, 1794518358664, 2862424846028174457, 5483249282630830360396, 39471589603944768518079950019, 3053134546009996125349281528007992109928
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A000178 = SUM[k=1..n] k^(k-1). A001923 = SUM[k=1..n] k^k. A061789 = SUM[k=1..n] p(k)^p(k), p(k) = k-th prime.
First differences a(n+1)-a(n) for n=1,...,9 are A076931(j) at j=3, 5, 7, 11, 13, 17, 19, 23 and 29. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 01 2007
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FORMULA
| a(n) = SUM[k=1..n] prime(k)^(prime(k)-2). a(n) = SUM[k=1..n] A000272(A000040(k)).
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EXAMPLE
| a(1) = number of labeled trees on prime(1) numbers of nodes = number of labeled trees on 2 nodes = A000272(2) = 2^0 = 1.
a(2) = number of labeled trees on prime(1) or prime(2) numbers of nodes = number of labeled trees on 2 or 3 nodes = A000272(2)+A000272(3) = 2^0 + 3^1 = 4.
a(3) = number of labeled trees on prime(1) or prime(2) or prime(3) numbers of nodes = number of labeled trees on 2 or 3 or 5 nodes = A000272(2)+A000272(3)+A000272(5) = 2^0 + 3^1 + 5^3 = 129.
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CROSSREFS
| Cf. A000040, A000178, A000272, A001923, A061789.
Sequence in context: A057134 A041495 A188315 * A001425 A050284 A096759
Adjacent sequences: A117894 A117895 A117896 * A117898 A117899 A117900
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 03 2006
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