A318199 a(n) is the largest integer m such that m^n <= n^prime(n).

1, 2, 6, 11, 34, 48, 112, 139, 274, 794, 860, 2125, 3259, 3313, 4842, 9741, 18637, 17946, 32306, 41558, 39471, 66148, 82046, 131305, 265464, 313781, 288660, 339008, 313761, 366288, 1287573, 1451134, 2014343, 1824089, 3743848, 3371509, 4510880, 5976406

Offset: 1

Author

Stefano Spezia, Aug 21 2018

Keywords

• nonn

Comments

The sequence is not monotonic, for example a(18) < a(17).

Conjecture: there is no run of consecutive increasing terms with more than 17 terms.

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A062481, A333138.

Programs

Maple

Digits:= 2000:
a:= n-> floor(n^(ithprime(n)/n)):
seq(a(n),n=1..40); # Muniru A Asiru, Sep 17 2018

Mathematica

a[n_]:=Floor[n^(Prime[n]/n)]; Array[a,40]

PARI

a(n) = sqrtnint(n^prime(n), n); \\ Michel Marcus, Mar 12 2020
vector(40, n, a(n))

Formula

a(n) = floor(n^(prime(n)/n)).

a(n) = floor(A062481(n)^(1/n)).