A247363 Central terms of triangle A247358.

1, 3, 16, 64, 343, 4096, 59049, 1000000, 14348907, 129140163, 1475789056, 38443359375, 1099511627776, 34271896307633, 1156831381426176, 42052983462257059, 1152921504606846976, 18446744073709551616, 295147905179352825856, 12116574790945106558976

Offset: 1

Author

Reinhard Zumkeller, Sep 14 2014

Keywords

• nonn

Comments

For all n there exist b(n) and e(n) such that: a(n)=b(n)^e(n) and b(n)+e(n)=2*n, see example.

Examples

			.   n |        a(n) | b(n)^e(n) | b(n)+e(n)
. ----+-------------+-----------+----------
.   1 |           1 |    1^1    |     2
.   2 |           3 |    3^1    |     4
.   3 |          16 |    2^4    |     6
.   4 |          64 |    2^6    |     8
.   5 |         343 |    7^3    |    10
.   6 |        4096 |    8^4    |    12
.   7 |       59049 |    9^5    |    14
.   8 |     1000000 |   10^6    |    16
.   9 |    14348907 |    3^15   |    18
.  10 |   129140163 |    3^17   |    20
.  11 |  1475789056 |   14^8    |    22
.  12 | 38443359375 |   15^9    |    24
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..400

Crossrefs

Cf. A247358, A000169.

Programs

Haskell

a247363 n = a247358 (2 * n - 1) n

PARI

row(n) = vecsort(vector(n, k, k^(n-k+1))); \\ A247358
a(n) = row(2*n-1)[n]; \\ Michel Marcus, Jan 24 2022

Python

def A247363(n):
    return(sorted((b+1)**((2*n-1)-b) for b in range(2*n-1))[n-1])
# Chai Wah Wu, Sep 14 2014

Formula

a(n) = A247358(2*n-1,n).