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Carmichael numbers of the form (12*k+1)*(24*k+1)*(36*k+1)*(72*k+1), where 12*k+1, 24*k+1, 36*k+1 and 72*k+1 are all primes.
2

%I #18 Sep 08 2022 08:46:11

%S 461574735553,84154807001953,973694665856161,3060522900274753,

%T 11861640972220321,386096840467598593,2322064552169233153,

%U 7545246852649391713,9688364125836900193,10972742858243841313,11660828668219467073,16553878978808515681,17905475062325518273

%N Carmichael numbers of the form (12*k+1)*(24*k+1)*(36*k+1)*(72*k+1), where 12*k+1, 24*k+1, 36*k+1 and 72*k+1 are all primes.

%H Amiram Eldar, <a href="/A255578/b255578.txt">Table of n, a(n) for n = 1..10000</a>

%H Umberto Cerruti, <a href="/A255578/a255578.pdf">Pseudoprimi di Fermat e numeri di Carmichael</a> (in Italian), p. 14.

%o (Magma) [(12*n+1)*(24*n+1)*(36*n+1)*(72*n+1): n in [1..4000] | IsPrime(12*n+1) and IsPrime(24*n+1) and IsPrime(36*n+1) and IsPrime(72*n+1)];

%Y Cf. A002997, A255218.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Feb 26 2015