A339974 - OEIS

%I #28 Dec 27 2020 19:32:13

%S 3,7,11,19,31,37,59,61,83,103,107,131

%N Odd primes that do not occur as the greatest prime divisor of any such odd composite k for which the odd part of phi(k) divides k-1.

%C Odd primes that do not occur as the greatest prime divisor (A006530) of any of the terms of A339880.

%C Naive way of computing (essentially an exhaustive search): apply A000523 to the terms of A339973, select unique values, add +2, and take the corresponding prime.

%C Questions: Is this sequence finite? If infinite, are there still only a finite number of 4k+1 primes (A002144) like 37 and 61?

%C a(13) >= 149, if it exists.

%e Prime 127 is NOT a member, because there exists a squarefree composite number 10697881195 = 5*29*53*97*113*127, for which A053575(10697881195) = A336466(10697881195) = 120393, which is a divisor of 10697881195-1. Note that 10697881195 is a term of A339880, but not that of A339870.

%Y Cf. A000523, A002144, A006530, A053575, A336466, A339870, A339880, A339973.

%Y Cf. also A339869.

%K nonn,more,hard

%O 1,1

%A _Antti Karttunen_, Dec 27 2020