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%I #18 Feb 15 2020 23:31:04
%S 50881,62033,67609,78761,95489,110449,120377,134521,140233,146761,
%T 162401,167977,170017,170969,179129,186337,195857,207281,218161,
%U 225913,234889,239513,246041,263177,266377,279497,285073,289153,290321,292009,299081,301801,312953
%N Product of exactly three distinct primes congruent to 1 mod 8 (A007519).
%C Subset of numbers that are divisible by exactly 3 primes (counted with multiplicity), also known as triprimes or 3-almost primes, A014612. Subset of {d = p_1 * p_2 * ... * p_m where p_i == 1 (mod 8), 1 <= i <= m are distinct primes} as occurs in Wei, p.2.
%H Charles R Greathouse IV, <a href="/A185379/b185379.txt">Table of n, a(n) for n = 1..10000</a>
%H Dasheng Wei, <a href="http://arxiv.org/abs/1102.3811">On the equation x^2-Dy^2=n</a>, Feb 18, 2011.
%F {A007519(i) * A007519(j) * A007519(k) for i < j < k}. {A000040(i) * A000040(j) * A000040(k) for i < j < k, and A000040(i) in A017077 and A000040(j) in A017077 and A000040(k) in A017077}.
%e a(12) = 170017 = 17 * 73 * 137 = A007519(1) * A007519(3) * A007519(7).
%t p = Select[Prime[Range[100]], Mod[#, 8] == 1 &]; Sort[Reap[Do[n = p[[i]] p[[j]] p[[k]]; If[n <= p[[1]] p[[2]] p[[-1]], Sow[n]], {i, 2, Length[p]}, {j, i - 1}, {k, j - 1}]][[2, 1]]]
%o (PARI) list(lim)=my(v=List(),u=v,t); forprime(p=2,lim\697, if(p%8==1, listput(u,p))); for(i=1,#u-2, for(j=i+1, #u-1, if(u[i]*u[j]*u[j+1]>lim, break); for(k=j+1,#u, t=u[i]*u[j]*u[k]; if(t>lim, break); listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Jan 31 2017
%Y Cf. A007519, A014612, A017077, A185377.
%K nonn,easy
%O 1,1
%A _Jonathan Vos Post_, Feb 20 2011
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