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 A225507 #23 Feb 16 2025 08:33:19 %S A225507 9,21,45,63,105,117,273,285,585,627,765,1365,1449,1677,3705,3885,4221, %T A225507 4485,4797,7137,7565,8109,10197,10545,11445,13065,14637,16965,19437, %U A225507 20805,26061,27645,30573,31317,33705,35853,38805,39897,40887,41181,48633,50505,57057 %N A225507 -3-Knödel numbers. %C A225507 Extension of k-Knödel numbers to k negative, in this case equal to -3. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+3) = 1 mod n. %H A225507 Amiram Eldar, <a href="/A225507/b225507.txt">Table of n, a(n) for n = 1..1000</a> %H A225507 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnoedelNumbers.html">Knödel Numbers</a> %p A225507 with(numtheory); ListA225507:=proc(q,k) local a,n,ok; %p A225507 for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do %p A225507 if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi; %p A225507 od; if ok=1 then print(n); fi; fi; od; end: ListA225507(10^6,-3); %t A225507 Select[Range[10000], CompositeQ[#] && Divisible[# + 3, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Mar 28 2019 *) %Y A225507 Cf. A208728. %Y A225507 Cf. A225506, A225508, A225509, A225510, A225511, A225512, A225513, A225514. %K A225507 nonn %O A225507 1,1 %A A225507 _Paolo P. Lava_, May 09 2013 %E A225507 Incorrect comment deleted by _Joseph DeVincentis_, Dec 04 2015 %E A225507 More terms from _Amiram Eldar_, Mar 28 2019