A005939 -id:A005939 - cp's OEIS frontend

A306449 Pseudoprimes to base 10 that are not squarefree.

9, 99, 657, 909, 1233, 11169, 13833, 19503, 20961, 23661, 51291, 69921, 90009, 99297, 109737, 139329, 203841, 237169, 256059, 321201, 339021, 346473, 460251, 475641, 686169, 760761, 927081, 1080801, 1621089, 1679931, 3100833, 3316941, 3845601, 3846051, 3942657, 4095081, 4281057

Offset: 1

Jianing Song, Feb 16 2019

nonn

Numbers k that are not squarefree and satisfy 10^(k-1) == 1 (mod k).
Any term is divisible by the square of a base-10 Wieferich prime (A045616 = {3, 487, 56598313, ...}).
Intersection of A005939 and A013929.

Amiram Eldar, Table of n, a(n) for n = 1..1000

Pseudoprimes to base b that are not squarefree: A158358 (b=2), A244065 (b=3), A243010 (b=5), A243089 (b=7), A243090 (b=8), A306448 (b=9), this sequence (b=10).

Cf. also A045616, A005939, A013929.

for(n=1, 10^6, if(Mod(10, n)^(n-1)==1 && !issquarefree(n), print1(n, ", ")))

A020198 Pseudoprimes to base 70.

Original entry on oeis.org

69, 169, 213, 341, 377, 561, 671, 703, 781, 897, 949, 1441, 1541, 1633, 1649, 1891, 2001, 2201, 2701, 2769, 2873, 3053, 3201, 4061, 4331, 4371, 4899, 4901, 6001, 6177, 6409, 6681, 7449, 7991, 9301, 9361, 11661, 12121, 12209, 12337, 12441, 12673, 12881

Offset: 1

David W. Wilson

nonn

Composite numbers n such that 70^(n-1) == 1 (mod n). - Michel Lagneau, Feb 18 2012

Cf. A001567 (pseudoprimes to base 2).

base = 70; t = {}; n = 1; While[Length[t] < 100, n++; If[! PrimeQ[n] && PowerMod[base, n-1, n] == 1, AppendTo[t, n]]]; t (* T. D. Noe, Feb 21 2012 *)
Select[Range[10^4], Not[PrimeQ[#]] && PowerMod[70, # - 1, #] == 1 &] (* Alonso del Arte, Jun 12 2015, based on Farideh Firoozbakht's program for A005939 *)

forcomposite(n=4,1e6, if(Mod(70,n)^(n-1)==1, print1(n", "))) \\ Charles R Greathouse IV, Jun 12 2015

cp's OEIS Frontend

A306449 Pseudoprimes to base 10 that are not squarefree.

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