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

1,2

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]

Links

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

Formula

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

Example

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.

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 *)

Prog

(PARI) m=27; for(n=1, m, d=divisors(n^n); print1(d[n], ", ")) \\ Klaus Brockhaus, Aug 14 2006
(GAP)  List([1..30], n->DivisorsInt(n^n)[n]); # Muniru A Asiru, Mar 06 2019

Crossrefs

Cf. A000312.

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

Sequence in context: A191351 A324553 A230283 * A073904 A036879 A281389

Adjacent sequences: A121064 A121065 A121066 * A121068 A121069 A121070

Keyword

nonn

Author

Leroy Quet, Aug 10 2006

Extensions

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

Status

approved