A066676 Smallest number m such that phi(m) is a multiple of n-th primorial number, the product of first n primes.

3, 7, 31, 211, 2311, 60653, 1023053, 19417793, 446235509, 12939711677, 200560490131, 14841484883609, 608500576478849, 26165522997357677, 1229779567395958169, 65178316970529225209, 3845520700432469775917, 234576762719782814756597, 15716643102168462956621849

Offset: 1

Author

Labos Elemer, Dec 19 2001

Keywords

• nonn

Examples

			n = 8: a(8) = 19417793, phi(a(8)) = 19199380 = 2*9699690 = 2*2*3*5*7*11*13*17*19.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..25

Crossrefs

Cf. A000010, A002110, A066674, A066675, A066677, A066678.

Programs

Mathematica

nmax = 25;
A066676 = {};
pm = 1;
Do[
  pm *= Prime[n];
  sol = 0;
  If[PrimeQ[pm + 1],
   sol = pm + 1;
   ,
   sd = Select[Divisors[pm/2], # <= Sqrt[pm/2] &];
   Do[
    f1 = sd[[i]];
    f2 = pm/2/f1;
    If[PrimeQ[2 f1 + 1] && PrimeQ[2 f2 + 1],
     sol = (2 f1 + 1)*(2 f2 + 1);
     Break[];
     ];
     , {i, Length[sd], 1, -1}];
   ];
  AppendTo[A066676, sol];
  Print[{n, sol}];
   , {n, nmax}];
A066676 (* Ray Chandler, Oct 21 2011 *)

Formula

a(n) = Min{x : A000010(x) mod A002110(n) = 0}.

Extensions

a(9)-a(11) from Donovan Johnson, Oct 12 2011

a(12)-a(13) upper limits from Donovan Johnson confirmed as next terms, a(14)-a(19) added by Ray Chandler, Oct 21 2011