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

1,1

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.

Links

Table of n, a(n) for n=1..12.

Example

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.

Sequence in context: A092102 A158722 A202301 * A123080 A161387 A229086

Adjacent sequences: A339971 A339972 A339973 * A339975 A339976 A339977

Keyword

nonn,more,hard

Author

Antti Karttunen, Dec 27 2020

Status

approved