A225514 - OEIS

A225514

-10-Knödel numbers.

4, 6, 8, 10, 12, 14, 24, 26, 30, 50, 56, 102, 110, 150, 152, 182, 276, 330, 350, 494, 550, 650, 770, 962, 1190, 1230, 1430, 1550, 1650, 2550, 2870, 3050, 3410, 3752, 3770, 4510, 4550, 5270, 6150, 6650, 6710, 9230, 9350, 10010, 10850, 11526, 12710, 12950, 15950

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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.

LINKS

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

Eric Weisstein's World of Mathematics, Knödel Numbers

MAPLE

with(numtheory); ListA225514:=proc(q, k) local a, n, ok;

for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do

if gcd(a, n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;

od; if ok=1 then print(n); fi; fi; od; end: ListA225514(10^6, -10);

MATHEMATICA

Select[Range[10000], CompositeQ[#] && Divisible[# + 10, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

CROSSREFS

Cf. A208728.