A259923 a(n) = prime(n)^pi(n).

1, 3, 25, 49, 1331, 2197, 83521, 130321, 279841, 707281, 28629151, 69343957, 4750104241, 6321363049, 10779215329, 22164361129, 2488651484819, 3142742836021, 406067677556641, 645753531245761, 806460091894081, 1517108809906561, 186940255267540403, 350356403707485209, 760231058654565217

Offset: 1

Author

Ilya Gutkovskiy, Jul 09 2015

Keywords

• nonn

Examples

			For n = 1, a(1) = 2^0 = 1.
		

Crossrefs

Cf. A000040, A000720.

Cf. A062457.

Programs

Magma

[NthPrime(n)^#PrimesUpTo(n): n in [1..30]]; // Vincenzo Librandi, Aug 03 2015

Mathematica

Table[Prime[n]^PrimePi[n], {n, 1, 25}]

PARI

vector(30, n, prime(n)^primepi(n)) \\ Michel Marcus, Jul 09 2015

Formula

a(n) = A000040(n)^A000720(n).

a(n) ~ (n * log n)^(n/log(n)), by the prime number theorem.