A226326 a(n) = smallest k such that prime(n) is the n-th largest divisor of k.

2, 6, 20, 42, 154, 156, 306, 836, 552, 1044, 1488, 2960, 2460, 3870, 7050, 12084, 8496, 10248, 14070, 12780, 18396, 31284, 50796, 38448, 55872, 82416, 37080, 51360, 65400, 88140, 146304, 169776, 123300, 133440, 150192, 181200, 131880, 176040, 260520, 326970

Offset: 1

Author

Irina Gerasimova, Jun 04 2013

Keywords

• nonn

Examples

			a(5) = 165 because the divisors of 165 are (165, 55, 33, 15, 11, 5, 3, 1) and prime(5) = 11 is the 5th divisor of 165.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A225562.

Programs

Maple

with(numtheory):
a:= proc(n) local k, p; p:= ithprime(n);
      for k from p by p while tau(k)`)[n]<>p do od; k
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Jun 04 2013

Mathematica

a[n_] := Module[{k, p}, p = Prime[n]; For[k = p, DivisorSigma[0, k] < n || Reverse[Divisors[k]][[n]] != p, k = k + p]; k];
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Mar 25 2017, after Alois P. Heinz *)

PARI

a(n)=my(p=prime(n),k,d);while(k+=p, d=divisors(k); if(#d>=n && d[#d-n+1]==p, return(k))) \\ Charles R Greathouse IV, Jun 04 2013

Extensions

a(5) corrected, a(6)-a(40) from Charles R Greathouse IV, Jun 04 2013