OFFSET
1,1
COMMENTS
It suffices to check all bases 2 <= b <= (gpf(n)+1)/2.
Squarefree composite numbers n such that gpf(n)-1 divides n-1 (by analogy to the Korselt's criterion).
Gpf(n) is odd, so gpf(n)-1 is even. Therefore, n-1 is even so n is odd. - David A. Corneth, Sep 20 2016
These numbers have at least three prime factors. Carmichael numbers A002997 are a subsequence. So the sequence is infinite. - Thomas Ordowski and Altug Alkan, Sep 20 2016
First numbers with 3, 4, ... prime factors are 231 = 3 * 7 * 11, 4641 = 3 * 7 * 13 * 17, 31395 = 3 * 5 * 7 * 13 * 23, 1163085 = 3 * 5 * 7 * 11 * 19 * 53, 11996985 = 3 * 5 * 7 * 11 * 13 * 17 * 47, and 286140855 = 3 * 5 * 7 * 11 * 13 * 17 * 19 * 59. - Charles R Greathouse IV, Sep 20 2016
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
231 = 3*7*11 is a term because b^231 == b (mod 11) for every integer b.
45 = 3^2*5 is not a term because 45 is not squarefree although b^45 == b (mod 5) for every integer b.
MATHEMATICA
Select[Select[DeleteCases[Range[2, 22000], p_ /; PrimeQ@ p], SquareFreeQ], Divisible[# - 1, FactorInteger[#][[-1, 1]] - 1] &] (* Michael De Vlieger, Sep 20 2016 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski and Altug Alkan, Sep 20 2016
STATUS
approved