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

1,1

Links

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

Example

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.

Maple

with(numtheory):
a:= proc(n) local k, p; p:= ithprime(n);
      for k from p by p while tau(k)<n or
        sort([divisors(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 *)

Prog

(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

Crossrefs

Cf. A225562.

Sequence in context: A370494 A036689 A355390 * A139115 A193538 A121128

Adjacent sequences: A226323 A226324 A226325 * A226327 A226328 A226329

Keyword

nonn

Author

Irina Gerasimova, Jun 04 2013

Extensions

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

Status

approved