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

16, 216, 32768, 4782969, 100000000000, 106993205379072, 30491346729331195904, 22168378200531005859375, 4951760157141521099596496896, 2528731089327963353099650821015994368

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..10.

Formula

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

Example

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

Mathematica

Select[ Rest[ Range[ 18]], !PrimeQ[ # ] &]^Prime[ Range[18 - PrimePi[18] - 1]] (* Robert G. Wilson v, Oct 21 2005 *)
Module[{c=Select[Range[20], CompositeQ]}, #[[1]]^#[[2]]&/@Thread[ {c, Prime[ Range[ Length[c]]]}]] (* Harvey P. Dale, Apr 05 2019 *)

Crossrefs

Cf. A002808, A000040.

Sequence in context: A181247 A138454 A235758 * A137701 A080514 A081969

Adjacent sequences: A086647 A086648 A086649 * A086651 A086652 A086653

Keyword

easy,nonn

Author

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

Status

approved