A180197 a(n) is 2^(p*q) mod r for the n-th odd number with exactly 3 distinct prime factors p < q < r.

1, 10, 8, 2, 9, 5, 12, 16, 15, 10, 8, 5, 27, 7, 1, 12, 23, 2, 8, 17, 9, 12, 2, 2, 9, 10, 9, 11, 8, 1, 29, 14, 4, 2, 23, 18, 42, 11, 9, 3, 12, 12, 6, 5, 12, 8, 2, 37, 1, 64, 2, 48, 18, 13, 62, 16, 14, 15, 56, 66, 1, 33, 19, 15, 4, 16, 33, 52, 32, 9

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 16 2011

Keywords

• nonn
• look

Comments

The lines with negative slope appearing to rise out of plots is caused by pq = 15 and large r. - T. D. Noe, Jul 28 2011

Examples

			a(1) = 2^(3*5) mod 7 = 32768 mod 7 = 1 because A046389(1) = 105 = 3*5*7.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A046389.

Cf. A027746.

Programs

Haskell

import Data.List (nub)
a180197 n = a180197_list !! (n-1)
a180197_list = f 1 where
   f x = if length ps == 3 && nub ps == ps
         then (2 ^ (ps!!0 * ps!!1) `mod` ps!!2) : f (x+2) else f (x+2)
         where ps = a027746_row x
-- Reinhard Zumkeller, Jan 29 2014

Maple

b:= proc(n) option remember; local i, k, l;
       if n=1 then 3,5,7
       else for k from mul(i, i=b(n-1)) +2 by 2
              do l:= ifactors(k)[2];
                 if nops(l) = 3 and add(i[2], i=l) = 3
                    then break fi
              od; sort(map(i-> i[1], l))[]
       fi
    end:
a:= proc(n) option remember; local p, q, r;
      p,q,r:= b(n);
      2 &^ (p*q) mod r
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Jan 17 2011

Mathematica

Reap[For[n = 105, n < 2000, n += 2, f = FactorInteger[n] // Transpose; If[f[[2]] == {1, 1, 1}, {p, q, r} = f[[1]]; Sow[Mod[2^(p*q), r]]]]][[2, 1]] (* Jean-François Alcover, Oct 24 2016 *)

Extensions

More terms from Alois P. Heinz, Jan 17 2011