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A182518
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Carmichael numbers of the form C = p*(2p-1)*(3p-2)*(6p-5), where p is prime.
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1
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63973, 31146661, 703995733, 21595159873, 192739365541, 461574735553, 3976486324993, 10028704049893, 84154807001953, 197531244744661, 741700610203861, 973694665856161, 2001111155103061, 3060522900274753, 3183276534603733, 4271903575869601
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OFFSET
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1,1
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COMMENTS
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We get Carmichael numbers with four prime divisors for p = 7, 271, 337, 727, 1237, 1531, 2281, 3037, 3067.
We get Carmichael numbers with more than four prime divisors for p = 31, 67, 157, 577, 2131, 2731, 3301.
Note: we can see that p, 2p-1, 3p-2 and 6p-5 can all four be primes only for p = 6k+1 (for p = 6k+5, we get 2p-1 divisible by 3), so in that case the formula is equivalent to C = (6k+1)(12k+1)(18k+1)(36k+1).
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
E. W. Weisstein, Carmichael Number
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PROG
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(PARI) search(lim)={
my(v=List(), n, f);
forprime(p=7, lim,
n=p*(2*p-1)*(3*p-2)*(6*p-5)-1;
if(n%(p-1), next);
f=factor(2*p-1);
for(i=1, #f[, 1], if(f[i, 2]>1 || n%(f[i, 1]-1), next(2)));
f=factor(3*p-2);
for(i=1, #f[, 1], if(f[i, 2]>1 || n%(f[i, 1]-1), next(2)));
f=factor(6*p-5);
for(i=1, #f[, 1], if(f[i, 2]>1 || n%(f[i, 1]-1), next(2)));
listput(v, n+1)
);
Vec(v)
}; \\ Charles R Greathouse IV, Oct 02 2012
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CROSSREFS
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Sequence in context: A145437 A214758 A212882 * A182089 A217126 A054738
Adjacent sequences: A182515 A182516 A182517 * A182519 A182520 A182521
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KEYWORD
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nonn
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AUTHOR
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Marius Coman, May 03 2012
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STATUS
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approved
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