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A086650 n-th composite number raised to the n-th prime number. 3


%S 16,216,32768,4782969,100000000000,106993205379072,

%T 30491346729331195904,22168378200531005859375,

%U 4951760157141521099596496896,2528731089327963353099650821015994368

%N n-th composite number raised to the n-th prime number.

%C This sequence arises as a result of exponentiation using the terms of the sequence A002808 as the base and the terms of the sequence A000040 as the exponent. This sequence has the very special and rare property of double exponential growth, meaning that its rate of growth grows. This property is due to the unregular growth of the prime exponent in the generating function for this sequence.

%F a(n) = A002808(n)^A000040(n).

%e a(3)=8^5=32768 because 8 is the 3rd composite number and 5 is the 3rd prime number.

%t Select[ Rest[ Range[ 18]], !PrimeQ[ # ] &]^Prime[ Range[18 - PrimePi[18] - 1]] (* _Robert G. Wilson v_, Oct 21 2005 *)

%t Module[{c=Select[Range[20],CompositeQ]},#[[1]]^#[[2]]&/@Thread[ {c,Prime[ Range[ Length[c]]]}]] (* _Harvey P. Dale_, Apr 05 2019 *)

%Y Cf. A002808, A000040.

%K easy,nonn

%O 1,1

%A Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Jul 26 2003

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Last modified September 22 17:12 EDT 2021. Contains 347607 sequences. (Running on oeis4.)