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Carmichael numbers of the form C = (30n-17)*(90n-53)*(150n-89).
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%I #20 Feb 24 2023 02:37:02

%S 29341,1152271,34901461,64377991,775368901,1213619761,4562359201,

%T 8346731851,9293756581,48874811311,68926289491,72725349421,

%U 84954809611,147523256371,235081952731,672508205281,707161856941,779999961061

%N Carmichael numbers of the form C = (30n-17)*(90n-53)*(150n-89).

%C Note that in this sequence, 30n-17, 90n-53, and 150n-89 do not have to be prime.

%C Conjecture: The number C = (30n+13)*(90n+37)*(150n+61) is a Carmichael number if (but not only if) 30n+13, 90n+37 and 150n+61 are all three prime numbers.

%C The conjecture is checked for 0<n<130; the condition is satisfied for n = 0, 1, 5, 12, 14, 12, 27, 28, 49, 55, 56, 71, 83, 121, 125.

%C We got Carmichael numbers with more than three prime divisors for n = 4 and n = 119.

%C The conjecture is true (follows from Korselt's criterion). - _Charles R Greathouse IV_, Jul 05 2017

%H Charles R Greathouse IV, <a href="/A182133/b182133.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) K(n, c)=my(f=factor(c)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1

%o list(lim)=my(v=List(), C, n); while(n++ && (C=(30*n-17)*(90*n-53)*(150*n-89))<=lim, if(K(C, 30*n-17) && K(C, 90*n-53) && K(C, 150*n-89), listput(v, C))); Vec(v) \\ _Charles R Greathouse IV_, Jul 05 2017

%K nonn

%O 1,1

%A _Marius Coman_, Apr 14 2012

%E a(13) inserted by _Charles R Greathouse IV_, Jul 05 2017