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A182133 Carmichael numbers of the form C = (30n-17)*(90n-53)*(150n-89). 1
29341, 1152271, 34901461, 64377991, 775368901, 1213619761, 4562359201, 8346731851, 9293756581, 48874811311, 68926289491, 72725349421, 84954809611, 147523256371, 235081952731, 672508205281, 707161856941, 779999961061 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
The conjecture is true (follows from Korselt's criterion). - Charles R Greathouse IV, Jul 05 2017
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
PROG
(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
CROSSREFS
Sequence in context: A083740 A083739 A329538 * A182416 A232201 A251563
KEYWORD
nonn
AUTHOR
Marius Coman, Apr 14 2012
EXTENSIONS
a(13) inserted by Charles R Greathouse IV, Jul 05 2017
STATUS
approved

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Last modified July 19 20:58 EDT 2024. Contains 374436 sequences. (Running on oeis4.)