1,1

There are terms produced by this form that are not Carmichael numbers when all three factors are prime, e.g. k is 54, 106, 222, 294, 494, 512.... An alternative form (60*k+151)*(240*k+601)*(300*k+751) will always produce Carmichael numbers when all three factors are prime. - Jonathon Martodam, Dec 12 2025

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Carmichael Number

(A007304 INTERSECT A157956) INTERSECT A230722.

carmQ[n_] := CompositeQ[n] && Divisible[n - 1, CarmichaelLambda[n]]; v = {30, 120, 150}; Times @@ (v*# + 1) & /@ Select[Range[1000], AllTrue[(w = v*# + 1), PrimeQ] && carmQ[Times @@ w] &] (* Amiram Eldar, Nov 11 2019 *)

(Magma) [n : k in [1..593 by 2] | IsPrime(a) and IsPrime(b) and IsPrime(c) and IsOne(n mod CarmichaelLambda(n)) where n is a*b*c where a is 30*k+1 where b is 120*k+1 where c is 150*k+1];

Subsequence of A083739 and of A230722.

Cf. A002997, A007304, A157956.

Sequence in context: A183707 A256274 A158890 * A084071 A251615 A321706

Adjacent sequences: A230743 A230744 A230745 * A230747 A230748 A230749

Arkadiusz Wesolowski, Oct 29 2013

approved