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A066676 Smallest number m such that phi(m) is a multiple of n-th primorial number, the product of first n primes. 4
3, 7, 31, 211, 2311, 60653, 1023053, 19417793, 446235509, 12939711677, 200560490131, 14841484883609, 608500576478849, 26165522997357677, 1229779567395958169, 65178316970529225209, 3845520700432469775917, 234576762719782814756597, 15716643102168462956621849 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

CROSSREFS

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

Sequence in context: A083772 A093441 A087864 * A073917 A030521 A105767

Adjacent sequences:  A066673 A066674 A066675 * A066677 A066678 A066679

KEYWORD

nonn

AUTHOR

Labos Elemer, Dec 19 2001

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

STATUS

approved

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Last modified March 28 17:28 EDT 2020. Contains 333090 sequences. (Running on oeis4.)