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

710533, 915981, 1293337, 2134277, 3542533, 13747361, 161216021, 206304961, 284166877, 748419127, 968283247, 1265740717, 2582246701, 4297753027, 10891270501, 11176136947, 11273608417, 11606768801, 12169503061, 13321141597, 14241379237, 17005529227, 19600350001

Offset: 1

Author

Amiram Eldar, Jul 23 2021

Keywords

• nonn

Comments

a(1) = 710533 = 487 * 1459 has 2 distinct prime divisors.

a(2) = 915981 = 3 * 11 * 41 * 677 has 4 distinct prime divisors.

a(58) = 176529862601 = 2141 * 6421 * 12841 is the least term with 3 distinct prime divisors.

a(6884) = 15314196673937701 = 19 * 31 * 41 * 71 * 109 * 281 * 331 * 881 is the least term with 8 distinct prime divisors.

a(111) = 619303584901 is the least term k such that A003961(k) is also a term.

a(30430) = 507728732614597601 is the least term k such that both A003961(k) and A003961(A003961(k)) are also terms.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001567, A003961.

A346569 is a subsequence.

Programs

Mathematica

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[#]] &]