A121067 a(n) = the n-th divisor of n^n (when the positive divisors of n^n are written in order from smallest to largest).

1, 2, 9, 8, 625, 8, 117649, 128, 6561, 32, 25937424601, 27, 23298085122481, 112, 375, 32768, 48661191875666868481, 72, 104127350297911241532841, 250, 2401, 1024, 907846434775996175406740561329, 162, 59604644775390625, 2704, 2541865828329

Offset: 1

Author

Leroy Quet, Aug 10 2006

Keywords

• nonn

Comments

This is also the n-th divisor of n^(n-1); any divisor with a factor of p^n is preceded by n smaller powers of p in the divisor list. [Franklin T. Adams-Watters, Sep 21 2009]

Examples

			1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64,... is the beginning of the sequence of divisors of 6^6 = 46656. 8 is the 6th term of this sequence of divisors (which is sequence A114334), so a(6) = 8.
		

Links

• Charlie Neder, Table of n, a(n) for n = 1..388 (first 180 terms from Alois P. Heinz)

Crossrefs

Cf. A000312.

Cf. A000169. [Franklin T. Adams-Watters, Sep 21 2009]

Programs

GAP

List([1..30],n->DivisorsInt(n^n)[n]); # Muniru A Asiru, Mar 06 2019

Maple

a:= n-> sort([numtheory[divisors](n^(n-1))[]])[n]:
seq(a(n), n=1..30);  # Alois P. Heinz, Oct 09 2016

Mathematica

Table[Divisors[n^n][[n]], {n, 27}] (* Michael De Vlieger, Sep 19 2017 *)

PARI

m=27;for(n=1,m,d=divisors(n^n);print1(d[n],",")) \\ Klaus Brockhaus, Aug 14 2006

Formula

a(n) <= A020639(n)^n, with equality for n a prime power. - Charlie Neder, Mar 06 2019

Extensions

More terms from Joshua Zucker, Klaus Brockhaus and Jason Earls, Aug 11 2006