A339974 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.

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

Offset: 1

Author

Antti Karttunen, Dec 27 2020

Keywords

• nonn
• more
• hard

Comments

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

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.

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

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

Examples

			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.
		

Crossrefs

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

Cf. also A339869.