A070600 Largest number with n prime factors where all factors are less than or equal to n.

0, 4, 27, 81, 3125, 15625, 823543, 5764801, 40353607, 282475249, 285311670611, 3138428376721, 302875106592253, 3937376385699289, 51185893014090757, 665416609183179841, 827240261886336764177, 14063084452067724991009

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = A007917(n)^n for n>1. - Michel Marcus, Sep 24 2020

Example

a(2) = 4 (4=2*2 has 2 factors and 2 is the largest prime number <= 2).
a(3) = 27 (27=3*3*3 has 3 factors and 3 is the largest prime number <= 3).
a(4) = 81 (81=3*3*3*3 has 4 factors and 3 is the largest prime number <= 4).

Mathematica

a[n_] := If[n == 1, 0, If[PrimeQ[n], n, NextPrime[n, -1]]^n];
Array[a, 18] (* Jean-François Alcover, Sep 24 2020 *)

Prog

(PARI) a(n) = if (n==1, 0, precprime(n)^n); \\ Michel Marcus, Sep 24 2020

Crossrefs

Cf. A007917 (largest prime <= n).

Sequence in context: A266011 A015238 A298987 * A357841 A100488 A220019

Adjacent sequences: A070597 A070598 A070599 * A070601 A070602 A070603

Keyword

easy,nonn

Author

Jostein Trondal (jallamekk(AT)hotmail.com), May 13 2002

Status

approved