A121067 - OEIS

%I #29 Mar 06 2019 16:00:52

%S 1,2,9,8,625,8,117649,128,6561,32,25937424601,27,23298085122481,112,

%T 375,32768,48661191875666868481,72,104127350297911241532841,250,2401,

%U 1024,907846434775996175406740561329,162,59604644775390625,2704,2541865828329

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

%C 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]

%H Charlie Neder, <a href="/A121067/b121067.txt">Table of n, a(n) for n = 1..388</a> (first 180 terms from Alois P. Heinz)

%F a(n) <= A020639(n)^n, with equality for n a prime power. - _Charlie Neder_, Mar 06 2019

%e 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.

%p a:= n-> sort([numtheory[divisors](n^(n-1))[]])[n]:

%p seq(a(n), n=1..30);  # _Alois P. Heinz_, Oct 09 2016

%t Table[Divisors[n^n][[n]], {n, 27}] (* _Michael De Vlieger_, Sep 19 2017 *)

%o (PARI) m=27;for(n=1,m,d=divisors(n^n);print1(d[n],",")) \\ _Klaus Brockhaus_, Aug 14 2006

%o (GAP)  List([1..30],n->DivisorsInt(n^n)[n]); # _Muniru A Asiru_, Mar 06 2019

%Y Cf. A000312.

%Y Cf. A000169. [_Franklin T. Adams-Watters_, Sep 21 2009]

%K nonn

%O 1,2

%A _Leroy Quet_, Aug 10 2006

%E More terms from _Joshua Zucker_, _Klaus Brockhaus_ and _Jason Earls_, Aug 11 2006