A185377 Product of exactly two distinct primes congruent to 1 mod 8 (A007519).

697, 1241, 1513, 1649, 1921, 2329, 2993, 3281, 3649, 3961, 3977, 4097, 4369, 4633, 4777, 5321, 5617, 5729, 6001, 6497, 6817, 6953, 7081, 7361, 7633, 7769, 7913, 8249, 8633, 8857, 9553, 9673, 9809, 9881, 10001, 10057, 10081, 10217, 10489, 10537

Offset: 1

Author

Jonathan Vos Post, Feb 20 2011

Keywords

• nonn
• easy

Comments

Subset of semiprimes A001358. 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.

Examples

			10001 is in this sequence because 10001 = 73 * 137 = A007519(3) * A007519(7).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Dasheng Wei, On the equation x^2-Dy^2=n, Feb 18, 2011.

Crossrefs

Cf. A000040, A001358, A007519, A017077.

Programs

Mathematica

p = Select[Prime[Range[200]], Mod[#, 8] == 1 &]; Sort[Reap[Do[n=p[[i]] p[[j]]; If[n <= p[[1]]p[[-1]], Sow[n]], {i, 2, Length[p]}, {j, i - 1}]][[2,1]]]

PARI

list(lim)=my(v=List(),P=List(),t); forprime(p=2,lim\17, if(p%8==1, listput(P,p))); for(i=2,#P, my(p=P[i]); for(j=1,i-1, t=p*P[j]; if(t>lim, break); listput(v,t))); Set(v) \\ Charles R Greathouse IV, Jul 03 2016

Formula

{A007519(i) * A007519(j) for i < j}.

{A000040(i) * A000040(j) for i < j, and A000040(i) in A017077 and A000040(j) in A017077}.