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A182133
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Carmichael numbers of the form C = (30n-17)*(90n-53)*(150n-89).
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1
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29341, 1152271, 34901461, 64377991, 775368901, 1213619761, 4562359201, 8346731851, 9293756581, 48874811311, 68926289491, 72725349421, 84954809611, 147523256371, 235081952731, 672508205281, 707161856941, 779999961061
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OFFSET
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1,1
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COMMENTS
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Note that in this sequence, 30n-17, 90n-53, and 150n-89 do not have to be prime.
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.
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.
We got Carmichael numbers with more than three prime divisors for n = 4 and n = 119.
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LINKS
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PROG
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(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
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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