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A306450 Non-coprime pseudoprimes to base 3 (A306451) that are not squarefree. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 9 10:09 EDT 2022. Contains 356021 sequences. (Running on oeis4.)