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 A117897 Number of labeled trees on prime numbers of nodes through n-th prime. 1
 1, 4, 129, 16936, 2357964627, 1794518358664, 2862424846028174457, 5483249282630830360396, 39471589603944768518079950019, 3053134546009996125349281528007992109928 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A000178 = Sum_{k=1..n} k^(k-1). A001923 = Sum_{k=1..n} k^k. A061789 = Sum_{k=1..n} prime(k)^prime(k), prime(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, May 01 2007 LINKS G. C. Greubel, Table of n, a(n) for n = 1..75 FORMULA a(n) = Sum_{k=1..n} prime(k)^(prime(k)-2). a(n) = Sum_{k=1..n} A000272(A000040(k)). 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. MATHEMATICA Table[Sum[Prime[k]^(Prime[k] -2), {k, n}], {n, 20}] (* G. C. Greubel, Sep 27 2021 *) PROG (Sage) [sum( nth_prime(k)^(nth_prime(k) -2) for k in (1..n)) for n in (1..20)] # G. C. Greubel, Sep 27 2021 CROSSREFS Cf. A000040, A000178, A000272, A001923, A061789. Sequence in context: A188315 A298274 A299136 * A001425 A050284 A096759 Adjacent sequences: A117894 A117895 A117896 * A117898 A117899 A117900 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, May 03 2006 STATUS approved

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Last modified June 8 13:50 EDT 2023. Contains 363165 sequences. (Running on oeis4.)