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Squarefree semiprimes which never occur in A245486.
1

%I #11 Mar 09 2020 22:10:19

%S 46,58,74,94,106,118,122,134,142,158,166,194,202,206,214,262,267,274,

%T 278,298,309,314,326,334,339,346,358,362

%N Squarefree semiprimes which never occur in A245486.

%C Also squarefree semiprimes which never occur in A332951.

%C This sequence is infinite. It appears that all terms can be divisible by 2 or 3.

%C If A014664(i) = A014664(j) for some 1 < i < j, then 2*prime(i) is a term. See A245486 for more information.

%H Romanian Master in Mathematics Contest, Bucharest, 2020, <a href="https://artofproblemsolving.com/community/c6h2019180">Problem 6</a>

%e a(2) = 58 because when 2^m - 1 or 2^m + 1 is divisible by 29, it's also divisible by 113. Therefore, there's no integer k such that A245486(k) = A006530(k) * A006530(k+1) = 58.

%Y Cf. A000040, A006530, A006881, A014664, A245486, A332951.

%K nonn,more

%O 1,1

%A _Jinyuan Wang_, Mar 04 2020