OFFSET
2,1
COMMENTS
The number of divisors of p^(n-1) is n times the number of prime factors of p^(n-1), where p is prime. It means that a solution exists for every n>1.
LINKS
Giovanni Resta, Table of n, a(n) for n = 2..100
EXAMPLE
a(10) = 432 because the number of divisors of 432 is 20, the number of different prime factors of 432 is 2 (2, 3), and 20 = 10 * 2.
MAPLE
with(numtheory): P:=proc(q) local k, n; for n from 2 to q do for k from 1 to 2^(n-1) do
if tau(k)=n*nops(factorset(k)) then print(k); break; fi; od; od; end: P(10^9);
MATHEMATICA
a[n_] := Block[{k = 2}, If[PrimeQ[n], 2^n/2, While[ DivisorSigma[0, k]/ PrimeNu[k] != n, k++]; k]]; a /@ Range[2, 25] (* Giovanni Resta, Nov 16 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Nov 15 2016
EXTENSIONS
a(29)-a(39) from Giovanni Resta, Nov 16 2016
STATUS
approved