A230746 Carmichael numbers of the form (30*k + 1)*(120*k + 1)*(150*k + 1), where 30*k + 1, 120*k + 1 and 150*k + 1 are all primes.

68154001, 3713287801, 63593140801, 122666876401, 193403531401, 227959335001, 246682590001, 910355497801, 4790779641001, 5367929037001, 6486222838801, 24572944746001, 25408177226401, 27134994772801, 55003376283001, 63926508701401, 108117809748001, 112614220996801

Offset: 1

Author

Arkadiusz Wesolowski, Oct 29 2013

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Carmichael Number
• Index entries for sequences related to Carmichael numbers
• Index entries for sequences related to pseudoprimes

Crossrefs

Subsequence of A083739 and of A230722.

Cf. A002997, A007304, A157956.

Programs

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]

Mathematica

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 *)

Formula

(A007304 INTERSECT A157956) INTERSECT A230722.