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The n-th number with n divisors.
2

%I #22 Aug 28 2021 00:08:29

%S 1,3,25,14,14641,44,24137569,70,1089,405,819628286980801,160,

%T 22563490300366186081,2752,9801,462,21559177407076402401757871041,

%U 1044,740195513856780056217081017732809,1520,141376,84992

%N The n-th number with n divisors.

%C Last element in n-th row of A073915.

%C a(p) = prime(p)^(p-1) for any prime number p. - _Paul Tek_, Jun 23 2013

%H T. D. Noe, <a href="/A073916/b073916.txt">Table of n, a(n) for n = 1..100</a>

%e For n = 4; the numbers with four divisors are 6, 8, 10, 14, 15, 21,... so a(4) = 14 because 14 is the 4th number with four divisors. - _Omar E. Pol_, Jun 01 2012

%t d = Table[Length[Divisors[n]], {n, 200000}]; t = {}; n = 0; ok = True; While[ok, n++; If[PrimeQ[n], AppendTo[t, Prime[n]^(n - 1)], c = Flatten[Position[d, n, 1, n]]; If[Length[c] >= n, AppendTo[t, c[[n]]], ok = False]]]; t (* _T. D. Noe_, Jun 23 2013 *)

%Y Cf. A073915.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Aug 18 2002

%E More terms from _Sascha Kurz_, Jan 28 2003

%E New name from _Omar E. Pol_, Jun 01 2012

%E a(22)-a(34) from _Paul Tek_, Jun 23 2013