This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A306259 #24 Feb 07 2019 20:06:49 %S A306259 21,105,165,205,231,273,301,341,385,465,561,609,645,651,861,889,903, %T A306259 1045,1065,1105,1265,1281,1365,1387,1491,1705,1729,1771,1785,1905, %U A306259 2041,2047,2145,2211,2265,2329,2359,2373,2465,2485,2665,2667,2701,2821,3045,3081,3165,3171,3201,3277 %N A306259 Composite numbers k such that 2^(k(k-1)) == 1 (mod k^2). %C A306259 Composites k such that A002326((k^2-1)/2) divides k(k-1). %C A306259 It contains all Fermat pseudoprimes to base 2, A001567. %C A306259 Since phi(p^2) = p(p-1), where p is a prime, then by Euler's theorem 2^(p(p-1)) == 1 (mod p^2) for every odd prime p. %H A306259 Robert Israel, <a href="/A306259/b306259.txt">Table of n, a(n) for n = 1..10000</a> %p A306259 filter:= k -> not isprime(k) and 2 &^ (k*(k-1)) mod (k^2) = 1: %p A306259 select(filter, [$4..10000]); # _Robert Israel_, Feb 07 2019 %t A306259 Select[Range[3300], And[CompositeQ@ #, PowerMod[2, # (# - 1), #^2] == 1] &] (* _Michael De Vlieger_, Feb 03 2019 *) %o A306259 (PARI) isok(k) = !isprime(k) && ((2^(k*(k-1)) % k^2) == 1); \\ _Michel Marcus_, Feb 01 2019 %Y A306259 Cf. A001567, A002326, A306270. %K A306259 nonn %O A306259 1,1 %A A306259 _Thomas Ordowski_, Feb 01 2019