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A346568 Fermat pseudoprimes to base 2 (A001567) k such that A003961(k) is also a Fermat pseudoprime to base 2.

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%I A346568 #9 Jul 24 2021 04:24:48
%S A346568 710533,915981,1293337,2134277,3542533,13747361,161216021,206304961,
%T A346568 284166877,748419127,968283247,1265740717,2582246701,4297753027,
%U A346568 10891270501,11176136947,11273608417,11606768801,12169503061,13321141597,14241379237,17005529227,19600350001
%N A346568 Fermat pseudoprimes to base 2 (A001567) k such that A003961(k) is also a Fermat pseudoprime to base 2.
%C A346568 a(1) = 710533 = 487 * 1459 has 2 distinct prime divisors.
%C A346568 a(2) = 915981 = 3 * 11 * 41 * 677 has 4 distinct prime divisors.
%C A346568 a(58) = 176529862601 = 2141 * 6421 * 12841 is the least term with 3 distinct prime divisors.
%C A346568 a(6884) = 15314196673937701 = 19 * 31 * 41 * 71 * 109 * 281 * 331 * 881 is the least term with 8 distinct prime divisors.
%C A346568 a(111) = 619303584901 is the least term k such that A003961(k) is also a term.
%C A346568 a(30430) = 507728732614597601 is the least term k such that both A003961(k) and A003961(A003961(k)) are also terms.
%H A346568 Amiram Eldar, <a href="/A346568/b346568.txt">Table of n, a(n) for n = 1..10000</a>
%e A346568 710533 = 487 * 1459 is a term since it is a Fermat pseudoprime to base 2, and A003961(710533) = 491 * 1471 = 722261 is also a Fermat pseudoprime to base 2.
%t A346568 psp = Cases[Import["https://oeis.org/A001567/b001567.txt", "Table"], {_, _}][[;; , 2]]; f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; pspQ[n_] := PowerMod[2, n - 1, n] == 1; Select[psp, pspQ[s[#]] &]
%Y A346568 Cf. A001567, A003961.
%Y A346568 A346569 is a subsequence.
%K A346568 nonn
%O A346568 1,1
%A A346568 _Amiram Eldar_, Jul 23 2021