%I #18 May 19 2023 13:23:57

%S 1,2,4,274,81,44

%N a(n) is the smallest tribonacci number (A000073) with exactly n divisors, or -1 if no such number exists.

%C a(8) = 24, a(10) = 745527911414639917440582097294401.

%C a(7), if it exists, is > A000073(200000). - _Vaclav Kotesovec_, May 17 2023

%C Has an infinite number of -1's for a(p) where p is prime as A000073 only contains a finite number of perfect powers (see Theorem 1 of Petho link). - _Michael S. Branicky_, May 17 2023

%H Attila Petho, <a href="https://www.emis.de/journals/AUSM/C2-1/math21-5.pdf">Fifteen problems in number theory</a>, Acta Univ. Sapientiae Math 2:1 (2010), 72-83.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TribonacciNumber.html">Tribonacci Number</a>.

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>.

%Y Cf. A000005, A000073, A005179, A081979.

%K nonn,more

%O 1,2

%A _Ilya Gutkovskiy_, May 14 2023