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A225514 -10-Knödel numbers.

%I A225514 #17 Feb 16 2025 08:33:19
%S A225514 4,6,8,10,12,14,24,26,30,50,56,102,110,150,152,182,276,330,350,494,
%T A225514 550,650,770,962,1190,1230,1430,1550,1650,2550,2870,3050,3410,3752,
%U A225514 3770,4510,4550,5270,6150,6650,6710,9230,9350,10010,10850,11526,12710,12950,15950
%N A225514 -10-Knödel numbers.
%C A225514 Extension of k-Knödel numbers to k negative, in this case equal to -10. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+10) = 1 mod n.
%H A225514 Amiram Eldar, <a href="/A225514/b225514.txt">Table of n, a(n) for n = 1..1000</a>
%H A225514 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnoedelNumbers.html">Knödel Numbers</a>
%p A225514 with(numtheory); ListA225514:=proc(q,k) local a,n,ok;
%p A225514 for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
%p A225514 if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
%p A225514 od; if ok=1 then print(n); fi; fi; od; end: ListA225514(10^6,-10);
%t A225514 Select[Range[10000], CompositeQ[#] && Divisible[# + 10, CarmichaelLambda[#]] &] (* _Amiram Eldar_, Mar 28 2019 *)
%Y A225514 Cf. A208728.
%Y A225514 Cf. A225506, A225507, A225508, A225509, A225510, A225511, A225512, A225513.
%K A225514 nonn
%O A225514 1,1
%A A225514 _Paolo P. Lava_, May 09 2013
%E A225514 More terms from _Amiram Eldar_, Mar 28 2019