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

%I A180197 #30 Jun 27 2024 22:16:00
%S A180197 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,
%T A180197 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,
%U A180197 16,14,15,56,66,1,33,19,15,4,16,33,52,32,9
%N A180197 a(n) is 2^(p*q) mod r for the n-th odd number with exactly 3 distinct prime factors p < q < r.
%C A180197 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
%H A180197 Alois P. Heinz, <a href="/A180197/b180197.txt">Table of n, a(n) for n = 1..20000</a>
%e A180197 a(1) = 2^(3*5) mod 7 = 32768 mod 7 = 1 because A046389(1) = 105 = 3*5*7.
%p A180197 b:= proc(n) option remember; local i, k, l;
%p A180197        if n=1 then 3,5,7
%p A180197        else for k from mul(i, i=b(n-1)) +2 by 2
%p A180197               do l:= ifactors(k)[2];
%p A180197                  if nops(l) = 3 and add(i[2], i=l) = 3
%p A180197                     then break fi
%p A180197               od; sort(map(i-> i[1], l))[]
%p A180197        fi
%p A180197     end:
%p A180197 a:= proc(n) option remember; local p, q, r;
%p A180197       p,q,r:= b(n);
%p A180197       2 &^ (p*q) mod r
%p A180197     end:
%p A180197 seq(a(n), n=1..70);  # _Alois P. Heinz_, Jan 17 2011
%t A180197 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 *)
%o A180197 (Haskell)
%o A180197 import Data.List (nub)
%o A180197 a180197 n = a180197_list !! (n-1)
%o A180197 a180197_list = f 1 where
%o A180197    f x = if length ps == 3 && nub ps == ps
%o A180197          then (2 ^ (ps!!0 * ps!!1) `mod` ps!!2) : f (x+2) else f (x+2)
%o A180197          where ps = a027746_row x
%o A180197 -- _Reinhard Zumkeller_, Jan 29 2014
%Y A180197 Cf. A046389.
%Y A180197 Cf. A027746.
%K A180197 nonn,look
%O A180197 1,2
%A A180197 _Juri-Stepan Gerasimov_, Jan 16 2011
%E A180197 More terms from _Alois P. Heinz_, Jan 17 2011