A306450 Non-coprime pseudoprimes to base 3 (A306451) that are not squarefree.

726, 1053426, 6498426, 7912311, 8141001, 190381521, 202730781, 283975626, 524245326, 767159481, 1095790641, 1620456321, 1904467521, 2287621281, 2700546486, 3462782961, 4120800321, 4928482581, 5816852481, 5974336401, 9313587921, 18723332001, 21215225361, 22073079666, 29882080866, 30132305841

Offset

1,1

Comments

Intersection of A306451 and A013929.

Terms must be divisible by the square of a Mirimanoff prime p (or base-3 Wieferich prime, A014127) such that the multiplicative order of 3 modulo p is not divisible by 3. So far, the only known Mirimanoff primes are 11 and 1006003. The multiplicative order of 3 modulo 11 is 5, not a multiple of 3, while the multiplicative order of 3 modulo 1006003 is 1006002, which is a multiple of 3. As a result, all known terms are divisible by 3*11^2 = 363.

Links

Table of n, a(n) for n=1..26.

Example

726 is a term because 726 divides 3^726 - 3 and 726 = 2 * 3 * 11^2.

Prog

(PARI) forstep(n=3, 10^9, 3, if(Mod(3, n)^n==3 && !issquarefree(n), print1(n, ", ")))

Crossrefs

Cf. A295740, A244065, A306451, A306452.

Sequence in context: A252617 A216618 A185527 * A259237 A084412 A090268

Adjacent sequences: A306447 A306448 A306449 * A306451 A306452 A306453

Keyword

nonn

Author

Jianing Song, Feb 16 2019

Extensions

More terms from Jinyuan Wang, Feb 18 2019

Status

approved