A306448 Pseudoprimes to base 9 that are not squarefree.

4, 8, 28, 52, 121, 364, 532, 616, 1036, 1288, 3052, 3751, 4376, 4636, 4961, 5356, 6364, 7381, 8744, 11011, 11476, 12124, 15964, 19096, 19684, 21196, 21736, 24388, 26596, 29161, 31876, 32791, 37576, 40132, 45676, 47972, 53092, 61831, 67276, 72136, 80476, 80956, 86296

Offset: 1

Author

Jianing Song, Feb 16 2019

Keywords

• nonn

Comments

Numbers k that are not squarefree and satisfy 9^(k-1) == 1 (mod k).

Any term is divisible by the square of a base-9 Wieferich prime ({2} U {base-3 Wieferich primes} = {2} U A014127 = {2, 11, 1006003, ...}).

Intersection of A020138 and A013929.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Pseudoprimes to base b that are not squarefree: A158358 (b=2), A244065 (b=3), A243010 (b=5), A243089 (b=7), A243090 (b=8), this sequence (b=9), A306449 (b=10).

Cf. also A014127, A020138, A013929.

Programs

PARI

for(n=1, 10^5, if(Mod(9, n)^(n-1)==1 && !issquarefree(n), print1(n, ", ")))